Chapter 4.8, Problem 34HP

To determine

Todraw:

An isosceles right triangle and label vertex.

Answer to Problem 34HP

The isosceles right triangle is,

  

Explanation of Solution

Sketch:

  

Interpretation:

If $\left(0,0\right)$ is the midpoint also $\left(a_1,b_1\right)$ and $\left(a_2,b_2\right)$ are the endpoint of the hypotenuse then $\left(0,0\right)=\left(\frac{a_1+a_2}{2},\frac{b_1+b_2}{2}\right)$ .

For this, to a true statement, $a_2=-a_1$ and $b_2=-b_1$ . This means the $x-$ and $y-$ coordinates of the endpoints will have opposite signs. If the two legs of the right triangle are constructed so that one is vertical segment will be $b-\left(-b\right)$ or $2b$ .

Since the triangle is isosceles, $2a=2b$ or $a=b$ . So, the $x-$ and $y-$ coordinates of the endpoints must have the same absolute values. Start by choosing endpoints for the hypotenuse that use the same number for the $x-$ and $y-$ values but have opposite signs in either endpoints.

So, say that $\left(-5,5\right)$ and $\left(5,-5\right)$ . The third point will be where the vertical and horizontal segments from the endpoints would intersect say at $\left(5,5\right)$ .