Calculating the length of a line with distance formula - GMAT Quantitative

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Question

What is the distance between the points and ?

Answer

Let's plug our coordinates into the distance formula.

$$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

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Question

What is the distance between the points and ?

Answer

We need to use the distance formula to calculate the distance between these two points.

$$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

Compare your answer with the correct one above

Question

A line segement on the coordinate plane has endpoints and . Which of the following expressions is equal to the length of the segment?

Answer

Apply the distance formula, setting

:

$d = $$\sqrt{(x_{2}$$- x_${1})^${2}$+(y_{2}$-y_${1})^{2}$}$

$d = $$\sqrt{[A-(A+4)]^{2}$$$+[(B+3)-B)]^{2}$}$

$d = $$\sqrt{(-4)^{2}$$$+3^{2}$} = $\sqrt{16+9}$ = $\sqrt{25}$ = 5$

Compare your answer with the correct one above

Question

What is distance between and ?

Answer

$distance= $$\sqrt{(x_{2}$$-x_${1})^$2$+y_{2}$-y_${1})^2$}$

$= $$\sqrt{(6-1)^2$$+(7-5)^2$}$$

$= $$\sqrt{(5)^2$$+(2)^2$}$$

$= $\sqrt{(25+4)}$$

$\sqrt{29}$

Compare your answer with the correct one above

Question

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

Find the length of segment $\overline{JK}$ .

Answer

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem.

$\small $d=$\sqrt{(x-x')^2$$+(y-y')^2$}$$

Plug in everthing and solve:

$\small \small $d=$\sqrt{(144-4)^2$$+(75-7)^2$}$=$\sqrt{24500}$\approx156.5$

So our answer is 156.6

Compare your answer with the correct one above

Question

What is the length of a line segment that starts at the point and ends at the point ?

Answer

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

$d=$\sqrt{(x_2-x_$1)^2$+(y_2-y_$1)^2$}$$

$d=$\sqrt{25}$$

Compare your answer with the correct one above

Question

What is the distance between the points and ?

Answer

Let's plug our coordinates into the distance formula.

$$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

Compare your answer with the correct one above

Question

What is the distance between the points and ?

Answer

We need to use the distance formula to calculate the distance between these two points.

$$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

Compare your answer with the correct one above

Question

A line segement on the coordinate plane has endpoints and . Which of the following expressions is equal to the length of the segment?

Answer

Apply the distance formula, setting

:

$d = $$\sqrt{(x_{2}$$- x_${1})^${2}$+(y_{2}$-y_${1})^{2}$}$

$d = $$\sqrt{[A-(A+4)]^{2}$$$+[(B+3)-B)]^{2}$}$

$d = $$\sqrt{(-4)^{2}$$$+3^{2}$} = $\sqrt{16+9}$ = $\sqrt{25}$ = 5$

Compare your answer with the correct one above

Question

What is distance between and ?

Answer

$distance= $$\sqrt{(x_{2}$$-x_${1})^$2$+y_{2}$-y_${1})^2$}$

$= $$\sqrt{(6-1)^2$$+(7-5)^2$}$$

$= $$\sqrt{(5)^2$$+(2)^2$}$$

$= $\sqrt{(25+4)}$$

$\sqrt{29}$

Compare your answer with the correct one above

Question

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

Find the length of segment $\overline{JK}$ .

Answer

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem.

$\small $d=$\sqrt{(x-x')^2$$+(y-y')^2$}$$

Plug in everthing and solve:

$\small \small $d=$\sqrt{(144-4)^2$$+(75-7)^2$}$=$\sqrt{24500}$\approx156.5$

So our answer is 156.6

Compare your answer with the correct one above

Question

What is the length of a line segment that starts at the point and ends at the point ?

Answer

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

$d=$\sqrt{(x_2-x_$1)^2$+(y_2-y_$1)^2$}$$

$d=$\sqrt{25}$$

Compare your answer with the correct one above

Question

What is the distance between the points and ?

Answer

Let's plug our coordinates into the distance formula.

$$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

Compare your answer with the correct one above

Question

What is the distance between the points and ?

Answer

We need to use the distance formula to calculate the distance between these two points.

$$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

Compare your answer with the correct one above

Question

A line segement on the coordinate plane has endpoints and . Which of the following expressions is equal to the length of the segment?

Answer

Apply the distance formula, setting

:

$d = $$\sqrt{(x_{2}$$- x_${1})^${2}$+(y_{2}$-y_${1})^{2}$}$

$d = $$\sqrt{[A-(A+4)]^{2}$$$+[(B+3)-B)]^{2}$}$

$d = $$\sqrt{(-4)^{2}$$$+3^{2}$} = $\sqrt{16+9}$ = $\sqrt{25}$ = 5$

Compare your answer with the correct one above

Question

What is distance between and ?

Answer

$distance= $$\sqrt{(x_{2}$$-x_${1})^$2$+y_{2}$-y_${1})^2$}$

$= $$\sqrt{(6-1)^2$$+(7-5)^2$}$$

$= $$\sqrt{(5)^2$$+(2)^2$}$$

$= $\sqrt{(25+4)}$$

$\sqrt{29}$

Compare your answer with the correct one above

Question

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

Find the length of segment $\overline{JK}$ .

Answer

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem.

$\small $d=$\sqrt{(x-x')^2$$+(y-y')^2$}$$

Plug in everthing and solve:

$\small \small $d=$\sqrt{(144-4)^2$$+(75-7)^2$}$=$\sqrt{24500}$\approx156.5$

So our answer is 156.6

Compare your answer with the correct one above

Question

What is the length of a line segment that starts at the point and ends at the point ?

Answer

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

$d=$\sqrt{(x_2-x_$1)^2$+(y_2-y_$1)^2$}$$

$d=$\sqrt{25}$$

Compare your answer with the correct one above

Question

What is the distance between the points and ?

Answer

Let's plug our coordinates into the distance formula.

$$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

Compare your answer with the correct one above

Question

What is the distance between the points and ?

Answer

We need to use the distance formula to calculate the distance between these two points.

$$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

Compare your answer with the correct one above

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Calculating the length of a line with distance formula - GMAT Quantitative

What is the distance between the points and ?

Let's plug our coordinates into the distance formula. $$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

What is the distance between the points and ?

We need to use the distance formula to calculate the distance between these two points. $$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

A line segement on the coordinate plane has endpoints and . Which of the following expressions is equal to the length of the segment?

Apply the distance formula, setting :

What is distance between and ?

Consider segment which passes through the points and . Find the length of segment .

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem. Plug in everthing and solve: So our answer is 156.6

What is the length of a line segment that starts at the point and ends at the point ?

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

What is the distance between the points and ?

Let's plug our coordinates into the distance formula. $$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

What is the distance between the points and ?

We need to use the distance formula to calculate the distance between these two points. $$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

A line segement on the coordinate plane has endpoints and . Which of the following expressions is equal to the length of the segment?

Apply the distance formula, setting :

What is distance between and ?

Consider segment which passes through the points and . Find the length of segment .

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem. Plug in everthing and solve: So our answer is 156.6

What is the length of a line segment that starts at the point and ends at the point ?

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

What is the distance between the points and ?

Let's plug our coordinates into the distance formula. $$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

What is the distance between the points and ?

We need to use the distance formula to calculate the distance between these two points. $$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

A line segement on the coordinate plane has endpoints and . Which of the following expressions is equal to the length of the segment?

Apply the distance formula, setting :

What is distance between and ?

Consider segment which passes through the points and . Find the length of segment .

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem. Plug in everthing and solve: So our answer is 156.6

What is the length of a line segment that starts at the point and ends at the point ?

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

What is the distance between the points and ?

Let's plug our coordinates into the distance formula. $$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

What is the distance between the points and ?

We need to use the distance formula to calculate the distance between these two points. $$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

Let's plug our coordinates into the distance formula.

$$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

We need to use the distance formula to calculate the distance between these two points.

$$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

Apply the distance formula, setting

:

$d = $$\sqrt{(x_{2}$$- x_${1})^${2}$+(y_{2}$-y_${1})^{2}$}$

$d = $$\sqrt{[A-(A+4)]^{2}$$$+[(B+3)-B)]^{2}$}$

$d = $$\sqrt{(-4)^{2}$$$+3^{2}$} = $\sqrt{16+9}$ = $\sqrt{25}$ = 5$

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

Find the length of segment $\overline{JK}$ .

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem.

$\small $d=$\sqrt{(x-x')^2$$+(y-y')^2$}$$

Plug in everthing and solve:

$\small \small $d=$\sqrt{(144-4)^2$$+(75-7)^2$}$=$\sqrt{24500}$\approx156.5$

So our answer is 156.6

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

$d=$\sqrt{(x_2-x_$1)^2$+(y_2-y_$1)^2$}$$

$d=$\sqrt{25}$$

Let's plug our coordinates into the distance formula.

$$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

We need to use the distance formula to calculate the distance between these two points.

$$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

Apply the distance formula, setting

:

$d = $$\sqrt{(x_{2}$$- x_${1})^${2}$+(y_{2}$-y_${1})^{2}$}$

$d = $$\sqrt{[A-(A+4)]^{2}$$$+[(B+3)-B)]^{2}$}$

$d = $$\sqrt{(-4)^{2}$$$+3^{2}$} = $\sqrt{16+9}$ = $\sqrt{25}$ = 5$

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

Find the length of segment $\overline{JK}$ .

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem.

$\small $d=$\sqrt{(x-x')^2$$+(y-y')^2$}$$

Plug in everthing and solve:

$\small \small $d=$\sqrt{(144-4)^2$$+(75-7)^2$}$=$\sqrt{24500}$\approx156.5$

So our answer is 156.6

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

$d=$\sqrt{(x_2-x_$1)^2$+(y_2-y_$1)^2$}$$

$d=$\sqrt{25}$$

Let's plug our coordinates into the distance formula.

$$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

We need to use the distance formula to calculate the distance between these two points.

$$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$

Apply the distance formula, setting

:

$d = $$\sqrt{(x_{2}$$- x_${1})^${2}$+(y_{2}$-y_${1})^{2}$}$

$d = $$\sqrt{[A-(A+4)]^{2}$$$+[(B+3)-B)]^{2}$}$

$d = $$\sqrt{(-4)^{2}$$$+3^{2}$} = $\sqrt{16+9}$ = $\sqrt{25}$ = 5$

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

Find the length of segment $\overline{JK}$ .

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem.

$\small $d=$\sqrt{(x-x')^2$$+(y-y')^2$}$$

Plug in everthing and solve:

$\small \small $d=$\sqrt{(144-4)^2$$+(75-7)^2$}$=$\sqrt{24500}$\approx156.5$

So our answer is 156.6

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

$d=$\sqrt{(x_2-x_$1)^2$+(y_2-y_$1)^2$}$$

$d=$\sqrt{25}$$

Let's plug our coordinates into the distance formula.

$$\sqrt{(2-7)^{2}$$$+(5-17)^{2}$}= $$\sqrt{(-5)^{2}$$$+(-12)^{2}$} = $\sqrt{25+144}$= $\sqrt{169}$ = 13

We need to use the distance formula to calculate the distance between these two points.

$$\sqrt{(1-5)^{2}$$$+(4-2)^{2}$} = $$\sqrt{(-4)^{2}$$$+(2)^{2}$} =$\sqrt{20}$=$\sqrt{4}$$\sqrt{5}$=2$\sqrt{5}$