Translate triangle a by vector (-3/1)to give triangle b. Then rotate your triangle b 180 degrees around the origin to give trian

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3 months ago

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gle. Describe fully the single transformation that maps triangle a onto triangle c

1 answer:

tester [12.3K] · Answer 1 · 2026-02-26T07:51:04+03:00

Answer:

Rotate triangle A about the point (1.5, -0.5) by 180°.

Step-by-step explanation:

Translating a figure by a vector $\binom{-3}{1}$ means shifting it 3 units left along the x-axis and 1 unit up along the y-axis.

The translation rule can be expressed as:

(x, y) → [(x - 3), (y + 1)]

Based on the provided figure,

The coordinates of triangle A are A(1, -1), B(1, -4) and C(3, -4)

Post-translation, the new coordinates are A'(-2, 0), B'(-2, -3), C'(0, -3).

Next, applying a 180° rotation to these new points about the origin gives:

Rotation rule:

(x, y) → (-x, -y)

A'(-2, 0) → A"(2, 0)

B'(-2, -3) → B"(2, 3)

C'(0, -3) → C"(0, 3)

Thus, the transformation A(1, -1) → A"(2, 0) represents the entire transformation.

The rule defining the transformation mapping triangle C to A would be expressed as:

Rotate triangle A about the point (1.5, -0.5) by 180°.