Question

A line segment AB has a midpoint M. If the endpoint B

is (5, -11) and the midpoint M is (-2,-6), what are the
coordinates of A?
Please explain your answer

Answer 1

To find the coordinates of point A, we use the midpoint formula, which leads to A having coordinates of (-9, -1) based on given midpoint M (-2, -6) and endpoint B (5, -11).

Step-by-step explanation:

To find the coordinates of point A when the midpoint M and endpoint B of a line segment AB are known, you can use the midpoint formula which states that the coordinates of the midpoint M are the averages of the coordinates of points A and B. The midpoint formula is:

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

Given M = (-2, -6) and B = (5, -11), let A = (x, y). By setting up equations based on the midpoint formula, we can find A:

-2 = (x + 5)/2

-6 = (y - 11)/2

Multiplying both sides of each equation by 2 gives us:

-4 = x + 5 and -12 = y - 11.

Solving for x and y:

x = -4 - 5 = -9

y = -12 + 11 = -1

Therefore, the coordinates of A are (-9, -1).