Midpoint Formula

Help Questions

ACT Math › Midpoint Formula

Questions 1 - 10

Janice and Mark work in a city with neatly gridded streets. If Janice works at the intersection of 33rd Street and 7th Avenue, and Mark works at 15th Street and 5th Avenue, how many blocks will they each travel to lunch if they meet at the intersection exactly in between both offices?

Explanation

Translating the intersections into points on a graph, Janice works at (33,7) and Mark works at (15,5). The midpoint of these two points is found by taking the average of the x-coordinates and the average of the y-coordinates, giving ((33+15)/2 , (5+7)/2) or (24, 6). Traveling in one direction at a time, the number of blocks from either office to 24th street is 9, and the number of blocks to 6th is 1, for a total of 10 blocks.

Suppose the midpoint of a line segment is What are the endpoints of the segment?

Explanation

The midpoint of a line segment is found using the formula $\left ( \frac{x_1+x_2 }{2}, \frac{y_1+y_2}{2}\right )$ .

The midpoint is given as Going through the answer choices, only the points and yield the correct midpoint of .

$\left ( \frac{2+6}{2}, \frac{8+16}{2} \right )=(4,12)$

Explanation

The midpoint of a line segment is . If one endpoint of the line segment is , what is the other endpoint?

Explanation

The midpoint formula can be used to solve this problem, where the midpoint is the average of the two coordinates.

$\text{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

We are given the midpoint and one endpoint. Plug these values into the formula.

$(4,-1)=(\frac{-4+x}{2},\frac{3+y}{2})$

$4=\frac{-4+x}{2}\ \text{and}\ -1=\frac{3+y}{2}$

Solve for the variables to find the coordinates of the second endpoint.

$8=-4+x\ \text{and}\ -2=3+y$

$12=x\ \text{and}\ -5=y$

The final coordinates of the other endpoint are .

Suppose the midpoint of a line segment is What are the endpoints of the segment?

Explanation

The midpoint of a line segment is found using the formula $\left ( \frac{x_1+x_2 }{2}, \frac{y_1+y_2}{2}\right )$ .

The midpoint is given as Going through the answer choices, only the points and yield the correct midpoint of .

$\left ( \frac{2+6}{2}, \frac{8+16}{2} \right )=(4,12)$

The midpoint of a line segment is . If one endpoint of the line segment is , what is the other endpoint?

Explanation

The midpoint formula can be used to solve this problem, where the midpoint is the average of the two coordinates.

$\text{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

We are given the midpoint and one endpoint. Plug these values into the formula.

$(4,-1)=(\frac{-4+x}{2},\frac{3+y}{2})$

$4=\frac{-4+x}{2}\ \text{and}\ -1=\frac{3+y}{2}$

Solve for the variables to find the coordinates of the second endpoint.

$8=-4+x\ \text{and}\ -2=3+y$

$12=x\ \text{and}\ -5=y$

The final coordinates of the other endpoint are .

What is the midpoint of MN between the points M(2, 6) and N (8, 4)?

(3, 5)

(5, 2)

(5, 5)

(3, 1)

(2, 1)

Explanation

The midpoint formula is equal to Actmath_21_285_q2 . Add the x-values together and divide them by 2, and do the same for the y-values.

x: (2 + 8) / 2 = 10 / 2 = 5

y: (6 + 4) / 2 = 10 / 2 = 5

The midpoint of MN is (5,5).

What is the midpoint of MN between the points M(2, 6) and N (8, 4)?

(3, 5)

(5, 2)

(5, 5)

(3, 1)

(2, 1)

Explanation

The midpoint formula is equal to Actmath_21_285_q2 . Add the x-values together and divide them by 2, and do the same for the y-values.

x: (2 + 8) / 2 = 10 / 2 = 5

y: (6 + 4) / 2 = 10 / 2 = 5

The midpoint of MN is (5,5).

On the real number line, what is the midpoint between $-7$ and $19$ ?

$6$

$13$

$-6$

$2$

$3$

Explanation

On the number line, $-7$ is $26$ units away from $19$ .

We find the midpoint of this distance by dividing it by 2.

$\frac{26}{2}=13$

To find the midpoint, we add this value to the smaller number or subtract it from the larger number.

$-7+13=6\ \text{or}\ 19-13=6$

The midpoint value will be $6$ .

On the real number line, what is the midpoint between $-7$ and $19$ ?

$6$

$13$

$-6$

$2$

$3$

Explanation

On the number line, $-7$ is $26$ units away from $19$ .

We find the midpoint of this distance by dividing it by 2.

$\frac{26}{2}=13$

To find the midpoint, we add this value to the smaller number or subtract it from the larger number.

$-7+13=6\ \text{or}\ 19-13=6$

The midpoint value will be $6$ .

Page 1 of 4

Return to subject