Question

Find the coordinates of D if E(-4,9) is the midpoint of DF with F(1,3).

Answer 1

To find the coordinates of point D when E is the midpoint of DF, and F's coordinates are known, use the midpoint formula which leads to D having coordinates (-9, 15).

Step-by-step explanation:

To find the coordinates of D, given that E(-4,9) is the midpoint of DF, with F having coordinates (1,3), we can use the midpoint formula:

The midpoint M(x,y) of a line segment with endpoints A(x1, y1) and B(x2, y2) is given by:

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

Since E is the midpoint of DF, we can set up the following equations:

• Ex = (Dx + Fx)/2
• Ey = (Dy + Fy)/2

Substituting the given values:

• -4 = (Dx + 1)/2
• 9 = (Dy + 3)/2

Solving for Dx and Dy yields:

• Dx = -4 * 2 - 1 = -9
• Dy = 9 * 2 - 3 = 15

Therefore, the coordinates of D are (-9, 15).