Write a coordinate proof to prove that the segment that joins the vertex angle of an isosceles triangle to the midpoint of its base is perpendicular to the base

Slope of the base segment line is zero, hence base segment is horizontal

Slope of the segment that joins the vertex angle to the midpoint of its base is undefined hence the line is vertical

Therefore, angle between base segment line and the segment line from the vertex angle to the midpoint is perpendicular

Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base

Step-by-step explanation:

Here we prove the required relation as follows;

Let the isosceles be ABC

The coordinates of the points are

C = (0, 0) (Vertex)

A =  (-a, b)

C = (a, b)

P = (0, b) (Midpoint of base)

Therefore, the gradient or slope of the base AC is presented as follows;

Hence, segment AC is vertical

Hence, segment CP is vertical

Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base.

a negative exponent is translated as follows:

so, we have

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x