ryanbraunsdorf10
Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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:

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.