Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (XY) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y)
midpoint (5. - 12), endpoint (4-7)
The other endpoint is
(Type an ordered pair)

Answer 1

Answer:

(6, -17)

Step-by-step explanation:

Given the coordinate of a midpoint, (5, -12), and one endpoint, (4, -7), the other endpoint can be determined as follows:

The midpoint formula is given as $M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$.

Since we are given ordered pairs of the midpoint and one endpoint, we would find the other ordered pair of the endpoint as shown below.

Let the other endpoint be $(x_1, y_1)$

Midpoint = M(5, -12)

Let the given endpoint = $(4, -7) = (x_2, y_2)$

Thus:

$M(5, -12) = (\frac{x_1 + 4}{2}, \frac{y_1 +(-7)}{2})$

Rewrite the equation to find the coordinates of the other endpoints

$5 = \frac{x_1 + 4}{2}$ and $-12 = \frac{y_1 - 7}{2}$

Solve for each:

$5 = \frac{x_1 + 4}{2}$

$5*2 = \frac{x_1 + 4}{2}*2$

$10 = x_1 + 4$

$10 - 4 = x_1 + 4 - 4$

$6 = x_1$

$x_1 = 6$

$-12 = \frac{y_1 - 7}{2}$

$-12*2 = \frac{y_1 - 7}{2}*2$

$-24 = y_1 - 7$

$-24 + 7 = y_1 - 7 + 7$

$-17 = y_1$

$y_1 = -17$

Ordered pair of the other endpoint is (6, -17)