Question

Graph the image of this figure after a dilation with a scale factor of 13 centered at the point (4, −2) .

Use the polygon tool to graph the dilated figure

Answer 1

Just took the test and got it right!

Explanation:

(look at the image down below :))

Answer 2

From the given triangle figure;

Labelled the triangle as A , B and C.

The coordinates of this triangle ABC are;

A = (1, 10) ,

B = (-2, 4)

C = (7, 4).

Given : Scale factor(k) =
`(1)/(3)` and centered at point (4, -2).

The rule of dilation with
`k= (1)/(3)` and center at point (4,-2) is:

`(x, y) \rightarrow ((1)/(3)(x-4)+4 , (1)/(3)(y+2)-2)`

`(x, y) \rightarrow ((1)/(3)x-(4)/(3)+4 , (1)/(3)y+(2)/(3)-2)`

or

`(x, y) \rightarrow ((1)/(3)x+(8)/(3) , (1)/(3)y-(4)/(3))`

then, the dilation of the given figure are;

`A(1, 10) \rightarrow ((1)/(3)\cdot 1+(8)/(3) , (1)/(3) \cdot 10-(4)/(3))` =
`((1)/(3)+(8)/(3) , (10)/(3)-(4)/(3))` =
`((9)/(3) , (6)/(3))` = A'(3 , 2)

`B(-2, 4) \rightarrow ((1)/(3)\cdot -2+(8)/(3) , (1)/(3) \cdot 4-(4)/(3))` =
`(-(2)/(3)+(8)/(3) , (4)/(3)-(4)/(3))` =
`((6)/(3) , (0)/(3))` =B'(2 , 0)

`C(7, 4) \rightarrow ((1)/(3)\cdot 7+(8)/(3) , (1)/(3) \cdot 4-(4)/(3))` =
`((7)/(3)+(8)/(3) , (4)/(3)-(4)/(3))` =
`((15)/(3) , (0)/(3))` = C'(5 , 0)

The coordinates of dilation images are:

A' = (3,2) , B' = (2, 0) and C' = (5, 0)

You can see the graph of the dilated image as shown below: