\(\overline{XY}\) is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of \(\overline{XY}\) is (-4,-2) find the coordinates of Y.
A
(-6,-2)
B
(0,8)
C
(4,10)
D
(0,4)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
The formula for midpoint = \(\frac{x_1 + x_2}{2}\), \(\frac{y_1 + y_2}{2}\)
(-4,-2) = (x,y)
x = \(\frac{x_1 + x_2}{2}\)
-4 = \(\frac{-8 + p}{2}\)
-4 * 2 = -8 + p
-8 + 8 = p
: p = 0
y = \(\frac{y_1 + y_2}{2}\)
-2 = \(\frac{-12 + q}{2}\)
-2 * 2 = -12 + q
-4 + 12 = q
: q = 8
Source: WAEC / JAMB / NECO Classroom Archive (Record #61431)