Question

The midpoint of segment AP is M(1,1). Find the coordinates of A given P(-3,0).

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

Answer 1

To find point A given midpoint M(1,1) and point P(-3,0), we use the midpoint formula, leading to the coordinates of point A being (5,2), which is option C.

Step-by-step explanation:

To find the coordinates of point A given that the midpoint of segment AP is M(1,1) and point P is (-3,0), we use the midpoint formula. The midpoint M of a segment with endpoints A(xA,yA) and P(xP,yP) is calculated using the formula:

M = ((xA+xP)/2, (yA+yP)/2)

Since we have M and P and are solving for A, we set up the equations:

1 = (xA-3)/2

1 = (yA+0)/2

Multiplying both sides of the equations by 2 gives us:

xA = 2 + 3 = 5

yA = 2 * 1 = 2

Thus, point A has coordinates A(5,2), which corresponds to option C.