Question

1. a square with vertices at (1,1), (1,3), (3,3), and (3,1) is dilated with a scale factor of 2 using the origin as the center. what are the coordinates of the new vertices?

o a. (2,2), (2,6), (6,6), (6,2)
o b. (1,2), (1,4), (3,4), (3,2)
o c. (0.5,0.5), (0.5,1.5), (1.5,1.5), (1.5,0.5)
o d. (2,2), (2,4), (4,4), (4,2)

Explanation:

Step1: Recall the dilation formula

When a point \((x,y)\) is dilated with a scale factor \(k\) and center at the origin \((0,0)\), the new point \((x',y')\) is given by \((x',y')=(kx,ky)\). Here \(k = 2\).

Step2: Apply the formula to each vertex

• For the vertex \((1,1)\): \((x',y')=(2\times1,2\times1)=(2,2)\)
• For the vertex \((1,3)\): \((x',y')=(2\times1,2\times3)=(2,6)\)
• For the vertex \((3,3)\): \((x',y')=(2\times3,2\times3)=(6,6)\)
• For the vertex \((3,1)\): \((x',y')=(2\times3,2\times1)=(6,2)\)

Answer:

a. \((2,2),(2,6),(6,6),(6,2)\)