Pentagon OPQRS is shown on the coordinate plane below:
Pentagon OPQRS on a coordinate plane with ordered pairs at O negative 1, 2, at P negative 5, 3, at Q negative 3, negative 2, at R 2, 1, and at S 2, 5.
If pentagon OPQRS is dilated by a scale factor of seven over four from the origin to create O′P′Q′R′S′, what is the ordered pair of point P′?
(−8.75, 5.25)
(−1.25, 0.75)
(−3.5, 8.75)
(−1.75, 3.5)
To find the new coordinates of point P' after dilating by a scale factor of 7/4 from the origin, we can multiply the x-coordinate and y-coordinate of point P by the scale factor.
Original coordinates of P: (-5, 3)
New x-coordinate of P': -5 * 7/4 = -35/4 = -8.75
New y-coordinate of P': 3 * 7/4 = 21/4 = 5.25
Therefore, the ordered pair of point P' is (-8.75, 5.25).
So, the correct answer is:
(−8.75, 5.25)