Question

the figure below shows rectangle abcd on a coordinate plane. if the rectangle is dilated by a scale factor of 2 with the origin as the center of dilation, what are the coordinates of vertex b of the dilated rectangle abcd? a (5, 5) b (10, 10) c (7.5, 7.5) d (30, 30)

Explanation:

Step1: Find original coordinates of B

From the graph, assume the original coordinates of B are \((5,5)\) (by counting grid - squares).

Step2: Apply dilation formula

For a dilation with scale factor \(k = 2\) and center at the origin \((0,0)\), the formula for dilation of a point \((x,y)\) is \((kx,ky)\). Here \(x = 5,y = 5,k = 2\), so the new coordinates are \((2\times5,2\times5)=(10,10)\).

Answer:

B. \((10,10)\)