ryanbraunsdorf10
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Triangle PQR has vertices P(−3,4), Q(−8,3), and R(−1,−6). Triangle PQR is dilated by a scale factor of 8 centered at the origin to get triangle P′Q′R′.
What are the coordinates of points P′, Q′, and R′ of the image?

P′(−38,−12), Q′(−1,38), R′(−18,−34)
P′(−3,32), Q′(−8,24), R′(−1,−48)
P′(−24,4), Q′(−64,3), R′(−8,−6)
P′(−24,32), Q′(−64,24), R′(−8,−48)

Sagot :

xero099

Answer:

The coordinates of points P', Q' and R' are (-24, 32), (-64, 24) and (-8,-48), respectively.

Step-by-step explanation:

Vectorially speaking, the dilation of a vector with respect to a given point is defined by the following formula:

[tex]P'(x,y) = O(x,y) + r\cdot [P(x,y)-O(x,y)][/tex], [tex]r > 1[/tex] (1)

Where:

[tex]O(x,y)[/tex] - Point of reference.

[tex]P(x,y)[/tex] - Original point.

[tex]P'(x,y)[/tex] - Dilated point.

[tex]r[/tex] - Scale factor.

If we know that [tex]O(x,y) = (0,0)[/tex], [tex]P(x,y) = (-3, 4)[/tex], [tex]Q(x,y) = (-8,3)[/tex], [tex]R(x,y) = (-1,-6)[/tex] and [tex]r = 8[/tex], then the new coordinates of the triangle are, respectively:

[tex]P'(x,y) = (0,0) + 8\cdot [(-3,4)-(0,0)][/tex]

[tex]P'(x,y) = (-24, 32)[/tex]

[tex]Q'(x,y) = (0,0) + 8\cdot [(-8,3)-(0,0)][/tex]

[tex]Q'(x,y) = (-64, 24)[/tex]

[tex]R'(x,y) = (0,0) + 8\cdot [(-1,-6)-(0,0)][/tex]

[tex]R'(x,y) = (-8,-48)[/tex]

The coordinates of points P', Q' and R' are (-24, 32), (-64, 24) and (-8,-48), respectively.

Answer:

(-24, 32), (-64, 24) and (-8,-48)

Step-by-step explanation:

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