Question

Graph Quadrilateral ABCD whose vertex matrix is shown below. Then graph the dilation of Quadrilateral ABCD with a scale factor of 3 on the same coordinate grid.

Answer 1

A

Explanation:

Edge 2020

Answer 2

The coordinates of the vertices of the dilated figure are:

A' is (-3 , 6), B' is (15 , 15), C' is (15 , 9), D' is (-12 , -3) ⇒ the answer is (a)

Explanation:

* Lets study the matrix of the dilation

- If we dilate any point by scale factor k we multiply the

coordinates of the point by k

- The matrix of the dilation by scale factor k is

`\left[\begin{array}{cc}k&0\\0&k\end{array}\right]`

* Now lets solve the problem

- We will multiply the matrix of dilation by the matrix of the

vertices of the quadrilateral

- The dimension of the matrix of the dilation is 2×2 and the

dimension of the matrix of the vertices of the quadrilateral

is 2×4 then the dimension of the matrix of the image of the

quadrilateral is 2×4

∵ The scale factor is 3

∴ The matrix of dilation is
`\left[\begin{array}{cc}3&0\\0&3\end{array}\right]`

∵ The matrix of the vertices of the quadrilateral is

`\left[\begin{array}{cccc}-1&5&5&-4\\2&5&3&-1\end{array}\right]`

∴ The image of the quadrilateral is :

`\left[\begin{array}{cc}3&0\\0&3\end{array}\right]\left[\begin{array}{cccc}-1&5&5&-4\\2&5&3&-1\end{array}\right]=`

`\left[\begin{array}{cccc}(3)(-1)+(0)(2)&(3)(5)+(0)(5)&(3)(5)+(0)(3)&(3)(-4)+(0)(-1)\\(0)(-1)+(3)(2)&(0)(5)+(3)(5)&(0)(5)+(3)(3)&(0)(-4)+(3)(-1)\end{array}\right]`

`\left[\begin{array}{cccc}-3&15&15&-12\\6&15&9&-3\end{array}\right]`

∴ The image of point A' is (-3 , 6)

∴ The image of point B' is (15 , 15)

∴ The image of point C' is (15 , 9)

∴ The image of point D' is (-12 , -3)

* The answer is figure (a)