ryanbraunsdorf10
Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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:

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.