Question

Based on the shortest leg of the triangle illustrated, if a similar triangle on the coordinate plane has its shortest leg defined by the points (-2, 4) and (-6, 0), what is the third point?

Answer 1

(-2, -8)

Step-by-step explanation:

The similarity ratio is 2.

All corresponding sides of similar triangles are proportional.

Answer 2

In a triangle ,shortest leg is located in the coordinate plane at B (-2,4) and  C(-6,0).

Distance between two points in  two dimensional plane is given by =$\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2$

BC= $\sqrt{(-2 +6)^2+(4-0)^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}$

     = 4 × 1.414

     =   5.656

Let A (p,q), be the Third vertex of ΔA BC.There will be no single point. We can find the locus of point A.

Equation of line BC is :

$\frac{y-0}{x+6}=\frac{4-0}{-2+6} \\\\ y= x +6$

So,the third point that is Locus of point A ,will be no point lying on the line, →y= x +6.

Also, A Triangle is formed, when

Sum of two sides of triangle is greater than third side.

So,third point A will be such that,

1. AB +AC> BC

2. AB +BC> AC

3. AC +BC> AB