Question

Find Endpoint from Midpoint and Endpoint

The midpoint of AB is M(-5, -2). If the coordinates of A are (-3,4), what are the coordinates of B?
a) (-7, -8)
b) (-9, 10)
c) (-1, 6)
d) (1, -2)

Answer 1

By applying the midpoint formula and algebraic manipulation, we determined the coordinates of point B as (-7, -8), which is option (a).

Step-by-step explanation:

To find the coordinates of point B given the midpoint M(-5, -2) and one endpoint A(-3, 4), recall that the midpoint formula is given by:

M(x,y) = ((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints. We are given that (x1, y1) = (-3, 4) and we need to find (x2, y2), which will be the coordinates for point B.

Using the midpoint coordinates and the coordinates of A, we can set up two equations to find the coordinates of B as follows.

For the x-coordinate:

-5 = (-3 + x2)/2

Multiply both sides by 2: -10 = -3 + x2

Add 3 to both sides: -7 = x2

For the y-coordinate:

-2 = (4 + y2)/2

Multiply both sides by 2: -4 = 4 + y2

Subtract 4 from both sides: -8 = y2

Therefore, the coordinates for point B are (-7, -8), which corresponds to option (a).