Exercise 10 Page 643

When we calculate a segments length in a coordinate plane we should consider the following:

• It's easier to find the lengths of horizontal and vertical segments.
• It's easier to find the length of a segment if one endpoint is at the origin.

We can always place one point at the origin and another point along one of the axes. However, since this is not a right triangle, we cannot place the third point so that we get one vertical and one horizontal side. With that said let's start by creating the base of the triangle. We will place one point at the origin and another point 60 units to the right of the origin.

The height of an isosceles triangle bisects the base. therefore, to place the third point, we need to go 50 units up from the base's midpoint.

Since the legs of an isosceles triangle are congruent, it does not matter which one we calculate. To make it easy for us, we will choose the leg that's between (0,0) and (30,50).

d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)

SubstitutePoints

Substitute ( 30,50) & ( 0,0)

d = sqrt(( 30 - 0)^2 + ( 50 - 0)^2)

SubTerms

Subtract terms

d = sqrt(30^2 + 50^2)

CalcPow

Calculate power

d = sqrt(900+2500)

AddTerms

Add terms

d = sqrt(3400)

The legs have a side of sqrt(3400).