Chapter 4.3, Problem 52SPR

To determine

The measures of the sides and the type of the triangle.

Answer to Problem 52SPR

Isosceles triangle.

Explanation of Solution

Given:

The given vertices are:

  

Calculation:

The value of $\overline{JK}$ will be:

  $\begin{array}{l}\overline{JK}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \overline{JK}=\sqrt{{\left(12-9\right)}^2+{\left(14-9\right)}^2}\\ \overline{JK}=\sqrt{9+25}\\ \overline{JK}=\sqrt{34}\end{array}$

The value of $\overline{KL}$ will be:

  $\begin{array}{l}\overline{KL}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \overline{KL}=\sqrt{{\left(14-12\right)}^2+{\left(6-14\right)}^2}\\ \overline{KL}=\sqrt{68}\\ \overline{KL}=2\sqrt{17}\end{array}$

The value of $\overline{LJ}$ will be:

  $\begin{array}{l}\overline{LJ}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \overline{LJ}=\sqrt{{\left(9-14\right)}^2+{\left(9-6\right)}^2}\\ \overline{LJ}=\sqrt{25+9}\\ \overline{LJ}=\sqrt{34}\end{array}$

Two sides are same; hence, the triangle is isosceles triangle.