Write a rule for the translation pictured below.Triangle ABC: A (3, -1), B (7, -5), C (-2, -2)Triangle A'B'C': A' (-1, 4), B' (3, 0), C' (-6, 3)

Question

Write a rule for the translation pictured below.

Triangle ABC:
A (3, -1),
B (7, -5),
C (-2, -2)

Triangle A'B'C':
A' (-1, 4),
B' (3, 0),
C' (-6, 3)

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Solution

To find the rule for the translation, we need to determine how we get from the original points to the new points.

Calculate the horizontal shift (x-direction): Subtract the x-coordinate of A from the x-coordinate of A'. Do the same for B and B', and C and C'. If the rule is consistent, you should get the same result each time.

A'x - Ax = -1 - 3 = -4 B'x - Bx = 3 - 7 = -4 C'x - Cx = -6 - (-2) = -4

So, the rule for the x-direction is x - 4.

Calculate the vertical shift (y-direction): Subtract the y-coordinate of A from the y-coordinate of A'. Do the same for B and B', and C and C'. If the rule is consistent, you should get the same result each time.

A'y - Ay = 4 - (-1) = 5 B'y - By = 0 - (-5) = 5 C'y - Cy = 3 - (-2) = 5

So, the rule for the y-direction is y + 5.

Combine the rules for the x and y directions to get the rule for the translation. The rule is (x, y) -> (x - 4, y + 5). This means that each point of Triangle ABC is moved 4 units to the left and 5 units up to get the corresponding point in Triangle A'B'C'.

This problem has been solved

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