Question

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Describe the transformation from ΔPQR to ΔSTU. Is this a congruence or similarity transformation?

ΔPQR: P(4, 0), Q(2, -3), R(5, -4)
ΔSTU: S(-4, -5), T(-2, -2), U(-5. -1)

Answer 1

Rotation of 180° about the origin (0, 0) followed by a translation of 5 units down.

Congruence transformation.

Explanation:

Given vertices of ΔPQR:

• P = (4, 0)
• Q = (2, -3)
• R = (5, -4)

Given vertices of ΔSTU:

• S = (-4, -5)
• T = (-2, -2)
• U = (-5, -1)

From observation, the mapping rule the transforms ΔPQR to ΔSTU is:

• 
  `(x,y) \rightarrow (-x,y-5)`

Rotation of 180° about the origin (0, 0) followed by a translation of 5 units down.

This is a congruence transformation as the two triangles have the same shape and same size.

Answer 2

From the coordinates we can see the rule for this transformation:

• (x, y) → (- x, - y - 5)

This is a rotation by 180 degrees and translation 5 units down, therefore shape or size remain as is. So this is a congruence transformation.