Chapter 10.1, Problem 22E

To determine

To plot the points and form a triangle and to find its side lengths and classify the triangle.

Answer to Problem 22E

The side length of the triangle are $10.82,12,10.82$

The triangle formed is an isosceles triangle

Explanation of Solution

Given information:

Points of each side is given as $A(6,3),B(-3,9),C(-3,-3)$

Calculation:

To plot the points to form a triangle

Let the two points be $(x1,y1,)(x_2,y_2,)$

Distance between the two points $(x1,y1,)$ and $(x_2,y_2,)$ on a co-ordinate plane is-

  $\sqrt{{(x_2,x_1)}^2+{(y_2,y_1)}^2}$

To find the length of AB , use the above formula-

  $AB=\sqrt{{(-3-6)}^2+{(9-3)}^2}$

Now subtract the numbers inside the bracket, gives-

  $AB=\sqrt{{(9)}^2+{(6)}^2}$

To find the square multiply each number with the same number.

  $AB=\sqrt{81+36}$

Now add both the numbers

  $AB=\sqrt{117}$

The square root of 117 is- $10.82$

So side length of AB is $10.82$

To find the length of BC use the above formula-

  $BC=\sqrt{{(-3-(-3))}^2+{(-3-9)}^2}$

Now subtract the numbers inside the bracket,

  $BC=\sqrt{{(0)}^2+{(12)}^2}$

To find the square multiply each number with the same number.

  $BC=\sqrt{0+144}$

Add both the numbers

  $BC=\sqrt{144}$

The square root of 114 is- $12$

So side length of BC is $12$

To find the length of CA use the above formula-

  $CA=\sqrt{{(-6-(-3))}^2+{(3-(-3))}^2}$

Now subtract the numbers inside the bracket,

  $CA=\sqrt{{(9)}^2+{(6)}^2}$

To find the square multiply each number with the same number.

  $CA=\sqrt{81+36}$

Add both the numbers

  $CA=\sqrt{117}$

The square root of 117 is- $10.82$

So side length of CA is $10.82$

Conclusion- The side lengths of the triangle are $10.82,12,10.82$ . Since two sides are same the triangle formed isas isosceles triangle.