Question

look at the triangle below and draw a dilation scale factor 2:1 and point of dilation (0, 0)
a=(1,5)
c=(-3,2)
b=(2,-1)

Explanation:

Step1: Recall dilation formula

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

Step2: Dilate point A

For point $A=(1,5)$, using the formula $(x',y')=(k\cdot x,k\cdot y)$, we have $x'=2\times1 = 2$ and $y'=2\times5=10$. So the new point $A'=(2,10)$.

Step3: Dilate point B

For point $B=(2, - 1)$, $x'=2\times2 = 4$ and $y'=2\times(-1)=-2$. So the new point $B'=(4,-2)$.

Step4: Dilate point C

For point $C=(-3,2)$, $x'=2\times(-3)=-6$ and $y'=2\times2 = 4$. So the new point $C'=(-6,4)$.

Step5: Draw the dilated triangle

Plot the points $A'=(2,10)$, $B'=(4,-2)$ and $C'=(-6,4)$ on the coordinate - plane and connect them to form the dilated triangle.

Answer:

The new vertices of the dilated triangle are $A'=(2,10)$, $B'=(4,-2)$ and $C'=(-6,4)$. Plot these points and connect them to get the dilated triangle.