3a) The coordinate of R after dilation is; R' = (-6, 21)
3b) The coordinate of T after dilation is; T' = (1, 3)
5) A dilation by a scale factor of 2 followed by a translation right 1 up 3.
How to carry out dilation in Transformation?
3a) We are given the coordinates of the rectangle as;
Q(-2, -1), R(-2, 7), S(4, 7), T(4, -1)
Now, we are told that R(-2, 7) is dilated about the origin with a scale factor of 3. Thus;
R' = (-2 *3), (3 * 7)
R' = (-6, 21)
3b) We are now told that T(4, -1) is dilated by a scale factor of 1/2 with R as center of origin. R has a coordinate of (-2, 7). Thus;
Coordinate of T' = (-2, 7) + ¹/₂((4, -1) - (-2, 7))
Coordinate of T' = (-2, 7) + ¹/₂(6, -8)
Coordinate of T' = (-2, 7) + (3, -4)
Coordinate of T' = (1, 3)
5) We can see that LN is 2 units while L'N' is 4 units and so we can say scale factor in the transformation of ΔLMN to ΔL'M'N' is 2.
Now, if we apply scale factor of 2 to coordinates of N before transformation, we will have; 2(3, 1) = (6, 2)
Comparing to N' which is (5, 5) we can say that it was shifted up by 3 units and right by 1 unit.
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