Chapter 6.8, Problem 3CYU

To determine

To find: The coordinates of the said square MNOP, after a dilation by the scale factor 2.5.

Answer to Problem 3CYU

Coordinates of the said square MNOP after the said dilation be:

  $M\text{`}\left(0,0\right),N\text{`}\left(7.5,-7.5\right),O\text{`}\left(0,-15\right),P\text{`}(-7.5,-7.5)$

Or, option A is correct answer.

Explanation of Solution

Given information: 

Given the square MNOP with following vertices

  $M\left(0,0\right),N\left(3,-3\right),O\left(0,-6\right),P(-3,-3)$

that to be dilated by a scale factor 2.5 .

Concept used: In dilation with center at origin, each original coordinate $(x,y)$ is changed as:

  $\left(x,y\right)\to (cx,cy)$

Where, c is the scale factor of dilation.

Calculation:

It is given that scale factor c is 2.5, so based on above rule, dilated coordinates are calculated as:

  $\begin{array}{l}M`\left(0\times 2.5,0\times 2.5\right),N`\left(3\times 2.5,-3\times 2.5\right),O`\left(0\times 2.5,-6\times 2.5\right),P`\left(-3\times 2.5,-3\times 2.5\right)\\ =M\text{`}\left(0,0\right),N\text{`}\left(7.5,-7.5\right),O\text{`}\left(0,-15\right),P\text{`}(-7.5,-7.5)\end{array}$

Conclusion:

Thus, coordinates given in option A are required coordinates after said dilation.