Question

Point B is at (3,1). For which segment is B a midpoint? AC¯¯¯¯¯¯¯¯ with endpoints at A(1,−1) and C(8,6) AC¯¯¯¯¯¯¯¯ with endpoints at A(1,−1) and C(5,3) AD¯¯¯¯¯¯¯¯ with endpoints at A(1,−1) and C(6,4) AC¯¯¯¯¯¯¯¯ with endpoints at A(1,−1) and C(7,5)

Answer 1

The correct option is;

`\overline {AC}` with endpoints at A(1, -1) and C(5, 3)

Explanation:

The given coordinates of point B is (3, 1)

The coordinates of the midpoint (x, y) of a segment with ends (x₁, y₁) and (x₂, y₂) is given as follows;

x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2

We therefore analyze each option to get the segment for which the point B is the midpoint as follows;

For A(1, -1) and C(8, 6)

The midpoint is ((1 + 8)/2, (-1 + 6)/2) = (4.5, 2.5)

Therefore, the point B is not the midpoint of the segment A(1, -1) and C(8, 6)

For A(1, -1) and C(5, 3)

The midpoint is ((1 + 5)/2, (-1 + 3)/2) = (3, 1)

Therefore, the point B is the midpoint of the segment A(1, -1) and C(5, 3)

For A(1, -1) and C(6, 4)

The midpoint is ((1 + 6)/2, (-1 + 4)/2) = (3.5, 1.5)

Therefore, the point B is the not midpoint of the segment A(1, -1) and C(6, 4)

For A(1, -1) and C(7, 5)

The midpoint is ((1 + 7)/2, (-1 + 5)/2) = (4, 2)

Therefore, the point B is the not midpoint of the segment A(1, -1) and C(7, 5).