Chapter 8.2, Problem 8PSA

a

To determine

To find: The coordinate of K.

Answer to Problem 8PSA

The coordinate of K : (0, 9)

Explanation of Solution

Given information

Triangle OKM is a dilation of triangle OHJ, with a dilation ratio of 3:1 for each pair of corresponding sides

Formula used

Using dilation, coordinates will be 3 times

Calculation

Since, coordinates of H are (0, 3)

Using dilation ratio (3:1), we have coordinates of K : (0, 9)

b

To determine

To calculate: The lengths of sides of triangle OHJ

Answer to Problem 8PSA

The lengths of sides of triangle OJH are:3 units, 4 units, and 5 units

Explanation of Solution

Given information

Triangle OKM is a dilation of triangle OHJ, with a dilation ratio of 3:1 for each pair of corresponding sides

Formula used

Pythagoras theorem

Distance formula

Calculation

Coordinates of vertices of triangle OHJ are:

O: (0, 0); H: (0, 4) and J: (3, 0)

Therefore, sides of the triangle will be as:

  $\begin{array}{l}\text{OH=}\sqrt{{\left(0-0\right)}^2+{\left(4-0\right)}^2}=\sqrt{4^2}=4\text{units}\\ \text{HJ= }\sqrt{{\left(3-0\right)}^2+{\left(0-4\right)}^2}=\sqrt{3^2+4^2}=5\text{units}\\ \text{OJ=}\sqrt{{\left(3-0\right)}^2+{\left(0-0\right)}^2}=\sqrt{3^2}=3\text{units}\end{array}$

c

To determine

To find:The lengths of sides of triangle OKM

Answer to Problem 8PSA

The lengths of sides of triangle OKM will be 9 units, 12 units and 15 units

Explanation of Solution

Given information

Triangle OKM is a dilation of triangle OHJ, with a dilation ratio of 3:1 for each pair of corresponding sides

Formula used

Using dilation ratio given

Calculation

Using dilation ratio of 3:1

Sides of the triangle will be three times of the lengths of sides of triangle OHJ, i.e.,

OK: 9 units; OM: 12 units and MK: 15 units