Question

The midpoint of start overline, AB, end overline AB is M, left bracket, 4, comma, minus, 7, right bracketM(4,−7). If the coordinates of AA are left bracket, 7, comma, minus, 6, right bracket(7,−6), what are the coordinates of BB?

Answer 1

To find the coordinates of point B, we use the midpoint formula with A's coordinates (7, -6) and M's coordinates (4, -7), leading to B's coordinates being (1, -8).

Step-by-step explanation:

The question asks us to find the coordinates of point B given that the midpoint M of the line segment AB is (4, -7) and the coordinates of point A are (7, -6). To find the coordinates of B, we use the midpoint formula which states that the x-coordinate of the midpoint is the average of the x-coordinates of A and B, and the y-coordinate of the midpoint is the average of the y-coordinates of A and B.

By setting up the equations (x_A + x_B) / 2 = x_M and (y_A + y_B) / 2 = y_M, we can solve for B's coordinates. With A's coordinates (7, -6) and M's (4, -7), we get:

(7 + x_B) / 2 = 4 and (-6 + y_B) / 2 = -7.

Solving for x_B gives us:

(7 + x_B) = 8

x_B = 1

And solving for y_B gives us:

(-6 + y_B) = -14

y_B = -8

Therefore, the coordinates of point B are (1, -8).