Question

Point (2,3) is dilated by a scale factor of 3.5 from the center of dilation at the origin. Where does the point end up?

A) (7, 10.5)
B) (0.57, 1.71)
C) (6.5, 9.75)
D) (14, 21)

Answer 1

After dilating the point (2,3) by a scale factor of 3.5 from the origin, the new location of the point is (7, 10.5).

Step-by-step explanation:

The dilation of a point in coordinate geometry means multiplying the x and y coordinates by the scale factor when the center of dilation is at the origin (0,0). In this case, the point (2,3) is dilated by a scale factor of 3.5 from the center of dilation at the origin. Using the properties of dilation, we can find the new coordinates as follows:

• Multiply the x-coordinate (2) by the scale factor (3.5) to get the new x-coordinate: 2 * 3.5 = 7.
• Multiply the y-coordinate (3) by the scale factor (3.5) to get the new y-coordinate: 3 * 3.5 = 10.5.

Therefore, the new location of the point after dilation is (7, 10.5).