What series of transformations from △ABC to △DEF shows that △ABC≅△DEF ?

A . a reflection across the y-axis followed by a translation of 1 unit right and 2 units up

B . a clockwise rotation of 90° about the origin followed by a translation of 4 units right and 4 units up

C. a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down

D . a reflection across the line y = x followed by a positive rotation of 270° about the center

Question

13-03-2017
Mathematics

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What series of transformations from △ABC to △DEF shows that △ABC≅△DEF ?

A . a reflection across the y-axis followed by a translation of 1 unit right and 2 units up

B . a clockwise rotation of 90° about the origin followed by a translation of 4 units right and 4 units up

C. a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down

D . a reflection across the line y = x followed by a positive rotation of 270° about the center

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MsEHolt MsEHolt · Answer 1 · 2018-10-15T02:03:38+02:00

Answer:

C. a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down

Step-by-step explanation:

Our pre-image points are A(-4, 1); B(-6, 5); C(-1, 2). Our image points are D(-2, 3); E(-5, -6) and F(0, -3).

A reflection across the x-axis will negate the y-coordinate of each point; this will map

A(-4, 1)→(-4, -1)

B(-6, 5)→(-6, -5)

C(-1, 2)→(-1, -2)

Comparing these points to the points in ΔDEF, we can see that each x-coordinate is 1 lower than the image points and each y-coordinate is 1 higher than the image points. This means we want to subtract 1 from each x-coordinate and subtract 1 from each y-coordinate; this is done by a translation 1 unit right and 1 unit down.