Question

What are endpoints of a line segment that divides the triangle defined by the vertices (2, 2), (8, 0), and (8, 4) into two congruent triangles?

A. (5, 1) and (8, 4)
B. (5, 3) and (5, 1)
C. (8, 2) and (2, 2)
D. (8, 0) and (5, 3)

Answer 1

C. (8, 2) and (2, 2)

Explanation:

In the image attached you can observe the given triange, which is an isosceles triangle because vertex A is right at the middle of side BC.

Also, notice that segment AH is the one that divide the triangle in two equals parts.

According to the graph and the given coordinates the segment origins at (2.2) and ends at (8.2).

Therefore, the right answer is C.

Answer 2

Answer: Option 'B' is correct.

Explanation:

Since we have given that

triangle defined by the vertices (2, 2), (8, 0), and (8, 4)

We need to divide the triangle into two congruent triangles.

As we know that "Median " divides into two congruent triangles.

So, we will apply the formula of "Mid point of two coordinates":

So, Suppose (2,2) and (8,0)

`((2+8)/(2),(2+0)/(2))\\\\((10)/(2),(2)/(2))\\\\=(5,1)`

Suppose (2,2) and (8,4)

`=((8+2)/(2),(2+4)/(2))\\\\=(10)/(2),(6)/(2))\\\\=(5.3)`

Hence, Option 'B' is correct.