Question

Write the points of the image after dilating the figure by a scale factor of 1/2 with the center of dilation at the point (1, -2).

R (3,4)
S (3,-7)
T (8,-7)

A) R' (1.5,2), S' (1.5,-3.5), T' (4,-3.5)
B) R' (1.5,2), S' (1.5,-3.5), T' (4,-3.5)
C) R' (1.5,2), S' (1.5,-3.5), T' (4,-3.5)
D) R' (1.5,2), S' (1.5,-3.5), T' (4,-3.5)

Answer 1

The correct dilated coordinates for points R, S, and T after a dilation with a scale factor of 1/2 around the center (1, -2) are R' (2, 1), S' (2, -4.5), and T' (4.5, -4.5). The given answer options do not match these calculations, suggesting an error in the provided choices.

Step-by-step explanation:

To find the coordinates of the points after a dilation with a scale factor of 1/2 and center of dilation at (1, -2), you should subtract the center of dilation coordinates from the original points' coordinates, scale these differences, and then add the center of dilation coordinates back to these scaled values. The calculations for the points R (3,4), S (3,-7), and T (8,-7) are as follows:

• For R': (3 - 1) * 0.5 = 1, (4 + 2) * 0.5 = 3. Hence R' is (1 + 1, 3 - 2), which simplifies to (2, 1).
• For S': (3 - 1) * 0.5 = 1, (-7 + 2) * 0.5 = -2.5. Hence S' is (1 + 1, -2.5 - 2), which simplifies to (2, -4.5).
• For T': (8 - 1) * 0.5 = 3.5, (-7 + 2) * 0.5 = -2.5. Hence T' is (3.5 + 1, -2.5 - 2), which simplifies to (4.5, -4.5).

None of the given answer choices match this correct calculation, indicating there may have been a mistake or typo in the provided answer options.