ISEE Middle Level Quantitative Reasoning - Lines

What is the length of a line segment with end points and ?

Explanation

The length of a line segment can be determined using the distance formula:

$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$D=\sqrt{(3-6)^2+(5-1)^2}$

$D=\sqrt{-3^2+4^2}$

$D=\sqrt{9+16}=\sqrt{25}=5$

What is the length of a line with endpoints and .

Explanation

To find the length of this line, you can subtract to get . Since the y-coordinates are the same, you don't have to take any vertical direction into account. Therefore, you only look at the x-coordinates!

What is the length of a line with endpoints and .

Explanation

What is the length of a line segment with end points and ?

Explanation

The length of a line segment can be determined using the distance formula:

$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$D=\sqrt{(3-6)^2+(5-1)^2}$

$D=\sqrt{-3^2+4^2}$

$D=\sqrt{9+16}=\sqrt{25}=5$

Find the slope of a line that passes through and .

The slope is undefined.

Explanation

Use the slope formula to solve:

$m = \frac{y_{2} -y_{1}}{x_{2} - x_{1}}$

Given the following points.

The slope can be calculated as follows.

$m = \frac{-1 - (-1)}{3- (-5)}$

$m = \frac{0}{8}$

Because the coordinates were the same for points A and B, this would form a horizontal line. The slope of any horizontal line is

Find the slope of a line that passes through and .

The slope is undefined.

Explanation

Use the slope formula to solve:

$m = \frac{y_{2} -y_{1}}{x_{2} - x_{1}}$

Given the following points.

The slope can be calculated as follows.

$m = \frac{-1 - (-1)}{3- (-5)}$

$m = \frac{0}{8}$

Because the coordinates were the same for points A and B, this would form a horizontal line. The slope of any horizontal line is

If you stand on a giant number line at point , what is your distance from point ?

Explanation

The distance on a number line is the number of whole number places between two numbers. When you are going from a negative value to a positive one or vice versa, you must find the distance from that both points are then add them together. is spaces away from and is spaces away. To find the distance you then add your two values of and to get .