Chapter SH, Problem 2.11MPS

To determine

To calculate: To find the coordinates of figure after a dilation with a scale factor of $2$

Answer to Problem 2.11MPS

Coordinates of figure after dilation are $A^{\prime }\left(-4,2\right),B^{\prime }\left(2,6\right),C^{\prime }\left(6,4\right)$

Explanation of Solution

Given information: A quadrilateral has vertices $A\left(-2,1\right),B\left(1,3\right),C\left(3,2\right)$

Formula Used:

Dilation is an enlargement or reduction of any object by a scale factor

Let scale factor be $k$

Thus, new coordinate of point $\left(x,y\right)$ after dilation is given as

  $\left(kx,ky\right)$

Calculation:

Given quadrilateral has vertices $A\left(-2,1\right),B\left(1,3\right),C\left(3,2\right)$

Scale factor $=2$

New coordinates of quadrilateral are calculated as

  $\begin{array}{l}{A}^{\prime }=\left(2\times -2,2\times 1\right)=\left(-4,2\right)\\ B^{\prime }=\left(2\times 1,2\times 3\right)=\left(2,6\right)\\ C^{\prime }=\left(2\times 3,2\times 2\right)=\left(6,4\right)\end{array}$

Conclusion:

Hence, coordinates of figure after dilation are $A^{\prime }\left(-4,2\right),B^{\prime }\left(2,6\right),C^{\prime }\left(6,4\right)$