A, b and c are the vertices of one triangle. a has a coordinate of (4,6) b has a coordinate of (2,-2) c has a coordinate of (-2,-4) d is the midpoint of ab e is the midpoint of ac prove that de is parallel to bc you must show each stage of your working out.

Step-by-step explanation:

Given: The triangle with coordinate A(4,6), B(2,-2) and C(-2,-4). D is the mid point of AB and E is the mid point of AC.

To prove: DE is parallel to BC.

Construction: Join DE.

Proof: If we prove the basic proportionality theorem that is , then it proves that DE is parallel to BC.

Now, Mid Point D has coordinates= and Mid Point E has coordinates=

Now, AD=

DB=

AE=

EC=

Now,

=

Hence,

Thus, By basic proportionality theorem, DE is parallel to BC.

Step-by-step explanation:

If DE and BC are parallel, then they have the same slope.

We have

A(4, 6), B(2, -2), C(-2, -4)

The formula of a midpoint:

D is the midpoint of AB, and E is a midpoint of AC.

Calculate the coordinateso fo D and E:

The formula of a slope:

Calculate the formula of a DE and BC:

The slope DE and the slope BC are the same.

Therefore DE is parallel to BC.

many reason,

step-by-step explanation: