Question

what are the coordinates of x if w (1,1) is the midpoint of xy and y has coordinates (-4,5)?
a) (5,-4)
b) (\frac{3}{2},-2)
c) (-\frac{3}{2},3)
d) (6,-3)
need help?

Explanation:

Step1: Recall midpoint formula

The midpoint \( M(x_m, y_m) \) of two points \( X(x_1, y_1) \) and \( Y(x_2, y_2) \) is given by \( x_m=\frac{x_1 + x_2}{2} \), \( y_m=\frac{y_1 + y_2}{2} \). We know \( M = W(1,1) \) and \( Y(-4,5) \), let \( X=(x,y) \).

Step2: Solve for \( x \)

Using the x - coordinate formula: \( 1=\frac{x+(-4)}{2} \). Multiply both sides by 2: \( 2=x - 4 \). Add 4 to both sides: \( x=2 + 4=6 \).

Step3: Solve for \( y \)

Using the y - coordinate formula: \( 1=\frac{y + 5}{2} \). Multiply both sides by 2: \( 2=y + 5 \). Subtract 5 from both sides: \( y=2-5=-3 \).

Answer:

D. (6, - 3)