Question

Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P′Q′R′ has vertices P′(1, 0), Q′(0, −1), and R′(−2, −1). Plot triangles PQR and P′Q′R′ on your own coordinate grid. Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer

Answer 1

scale fact 1/4

Explanation:

Answer 2

Scale factor is
`(1)/(4)`.

Explanation:

Given the coordinates of
`\triangle PQR` as:

`P(4, 0)\\Q(0, -4)\\R(-8, -4)`

And the coordinates of
`\triangle P' Q' R'` as:

`P'(1, 0)\\Q'(0, -1)\\R'(-2, -1)`

To find:

The scaling factor of the dilation to transform the
`\triangle PQR` to
`\triangle P' Q' R'`.

Solution:

First of all, let us find the distance between the vertices i.e. the sides of the triangle.

Distance formula:

`D = √((x_2-x_1)^2+(y_2-y_1)^2)`

Where
`(x_1,y_1), (x_2,y_2)` are the coordinates of two points between which the distance is to be calculated.

`PQ = √(4^2+4^2) = 4\sqrt2`

`QR = √(8^2+0^2) = 8`

`PR = √(4^2+12^2) = 4√(10)`

Now, let us find the sides of the
`\triangle P' Q' R'`:

`P' Q' = √(1^2+1^2) = √(2)`

`Q' R' = √(2^2+0^2) = 2`

`P' R' = √(3^2+1^2) = √(10)`

We can clearly see that, the sides of
`\triangle PQR` are four times the corresponding sides of
`\triangle P' Q' R'`.

Therefore, the scaling factor is
`(1)/(4)`.

Please refer to the attache image in the answer area.