Question

Given A(-3, 8), find the coordinates of the point B such that C(5, -8) is the midpoint of segment AB.

Answer 1

We know that the coordinates of the midpoint are the average of the coordinates of the two endpoints.

So, we have

$C_x = \dfrac{A_x+B_x}{2},\quad C_y=\dfrac{A_y+B_y}{2}$

Plug the known values for A and C and solve each equation for the coordinates of point B:

$5 = \dfrac{-3+B_x}{2},\quad -8=\dfrac{8+B_y}{2}$

Multiply both equations by 2:

$10 = -3+B_x,\quad -8=8+B_y$

Subtract the known coordinate from each equation:

$13 = B_x,\quad -16=B_y$

So, the point B is $(13,-16)$

Answer 2

The midpoint of a segment divides the segment into equal halves.

The coordinates of point B is (13,-24)

Given that:

$(x_1,y_1) = (-3,8)$ --- point A

$(x,y) = (5,-8)$---- The midpoint

$B = (x_2,y_2)$

The midpoint is calculated as follows:

$(x.y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$

So, we have:

$(5,-8) = (\frac{-3 + x_2}{2}, \frac{8 + y_2}{2})$

Multiply through by 2

$(10,-16) = (-3 + x_2, 8 + y_2)$

By comparison, we have:

$-3 + x_2 = 10$ and $8 + y_2 = -16$

$-3 + x_2 = 10$

$x_2 = 10 + 3$

$x_2 = 13$

$8 + y_2 = -16$

$y_2 = -16 - 8$

$y_2 = -24$

Hence, the coordinates of point B is (13,-24)

Read more about midpoints at:

https://brainly.com/question/2441957