Question

the midpoint of ab is M(4,2). If the coordinates of A are (6,-4) what are the coordinates of B

Answer 1

We can use the midpoint formula:

Midpoint formula: Midpoint between two points (x₁, y₁) and (x₂, y₂) is:

((x₁ + x₂)/2, (y₁ + y₂)/2)

We know the midpoint (M) and one endpoint (A) of segment AB. Let's plug those values into the formula and solve for the unknown endpoint (B).

Let B = (x, y)

Midpoint formula:

((x₁ + x₂)/2, (y₁ + y₂)/2) = M(x, y)

((6 + x)/2, (-4 + y)/2) = (4, 2)

Simplify:

(6 + x)/2 = 4
(-4 + y)/2 = 2

Solve for x and y:

(6 + x)/2 = 4
6 + x = 8
x = 2

(-4 + y)/2 = 2
-4 + y = 4
y = 8

Therefore, the coordinates of point B are (2, 8).