Question

lesson 5 quiz performing and describing transformations involving dilations name: 1.josi sibemuye1 the quadrilateral shown on the coordinate grid below is a scale drawing for a wall of a birdhouse leo is designing. leo also wants to draw the size of the actual wall of the birdhouse on the grid by dilating the quadrilateral from the coordinate grid with a center at the origin and a scale factor of 2. draw the size of the actual wall of the birdhouse by dilating the figure on the coordinate grid with a center of dilation at the origin and a scale factor of 2. use the polygon tool to plot the actual wall of the birdhouse. a (2,5) a(4,10) b(5,4) b(10,8) c(2,1) c(4,2) d(5,1) d(10,2)

Explanation:

Step1: Recall dilation formula

When dilating a point $(x,y)$ with a center of dilation at the origin $(0,0)$ and a scale - factor $k$, the new point $(x',y')$ is given by $(x',y')=(k\times x,k\times y)$. Here $k = 2$.

Step2: Dilate point A

For point $A(2,5)$, using the formula $(x',y')=(k\times x,k\times y)$ with $k = 2$, we have $x'=2\times2 = 4$ and $y'=2\times5 = 10$. So the new point $A'$ is $(4,10)$.

Step3: Dilate point B

For point $B(5,4)$, $x'=2\times5 = 10$ and $y'=2\times4 = 8$. So the new point $B'$ is $(10,8)$.

Step4: Dilate point C

For point $C(2,1)$, $x'=2\times2 = 4$ and $y'=2\times1 = 2$. So the new point $C'$ is $(4,2)$.

Step5: Dilate point D

For point $D(5,1)$, $x'=2\times5 = 10$ and $y'=2\times1 = 2$. So the new point $D'$ is $(10,2)$.

Answer:

The new coordinates of the dilated quadrilateral are $A'(4,10)$, $B'(10,8)$, $C'(4,2)$, $D'(10,2)$. Plot these points using the Polygon tool.