Question

CD has a midpoint at M(-3, 5). Point C is at (-4, 7). Find the coordinates of point D.

A) D(1, 3)
B) D(-2, 3)
C) D(-2, 4)
D) D(1, 5)

Answer 1

To find the coordinates of point D, we use the midpoint formula with the given midpoint M(-3, 5) and point C (-4, 7). Upon calculation, the coordinates of point D are found to be (-2, 3), which corresponds to option B.

Step-by-step explanation:

The question is asking for the coordinates of point D given that CD has a midpoint at M(-3, 5) and point C is at (-4, 7). To find the coordinates of point D, we use the midpoint formula, which states that the midpoint M's coordinates are the average of the x-coordinates and y-coordinates of points C and D respectively.

Since M(-3, 5) is the midpoint, its coordinates are obtained as follows:

Mx = (Cx + Dx)/2 My = (Cy + Dy)/2

We can solve these equations for Dx and Dy, using the given coordinates of C and M.

Dx = 2Mx - Cx Dy = 2My - Cy

Substituting the given values, we get:

Dx = 2(-3) - (-4) = -6 + 4 = -2 Dy = 2(5) - 7 = 10 - 7 = 3

Therefore, the coordinates of point D areoption B) (-2, 3) .