Question

Given points A(2, 3) and B(-2,5), explain how you could use the Distance Formula and an indirect argument to show that point C(O, 3) is NOT the midpoint of AB.

Answer 1

Therefore C is not the midpoint of AB.

Explanation:

Midpoint: The midpoint is a point from which the distance between the endpoints of a line segment is always equal.

Distance formula:

The distance between the points (x₁,y₁) and (x₂,y₂) is

`√((x_2-x_1)^2+(y_2-y_1))`

Given points are A(2,3) and B(-2,5).

If C(0,3) is the midpoint of the line segment AB,then AC=BC.

The distance between AC is

`√((0-2)^2+(3-3)^2)`

`=√(2^2)`

=2 units

The distance between AC is

`√((0-(-2))^2+(3-5)^2)`

`=√(2^2+2^2)`

`=4√(2)` units.

Since AC ≠ BC

Therefore C is not the midpoint of AB.