Question

The midpoint of AB is M (-3,2). If the coordinates of A are (-1,-3), what are the coordinates of B?

a) (-5,7)
b) (-7,7)
c) (-5,3)
d) (-5,-7)

Answer 1

To find the unknown coordinates of point B when given the midpoint M and coordinates of point A, use the midpoint formula. After solving the equations satisfying the midpoint formula, we determine that the coordinates of point B are (-5,7).

Step-by-step explanation:

The question asks us to find the coordinates of point B if the midpoint M of AB is (-3,2) and the coordinates of A are (-1,-3). To find B, we can use the midpoint formula, which says that the midpoint M is the average of the x-coordinates and y-coordinates of A and B, respectively.

The midpoint formula is given by:

• Mx = (Ax + Bx) / 2
• My = (Ay + By) / 2

We can plug in the known values and solve for B:

-3 = (-1 + Bx) / 2

2 = (-3 + By) / 2

Multiplying each equation by 2 gives us:

-6 = -1 + Bx
Bx = -5

4 = -3 + By
By = 7

Therefore, the coordinates of B are (-5,7).