Question

Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.

Answer 1

The given reflection transformation is a rigid transformation, such that the dimensions are preserved

The statements that are true about the image of triangle ABC following a reflection Bout the the line y = 2·a are;

• AB = RS

• ΔABC ≅ ΔRST

• m∠BAC ≅ m∠SRT

Reasons:

The given parameters are;

Triangle ΔABC is reflected across the line y = 2·x

Given that a reflection is a rigid transformation, we have;

The distance between two points on a preimage is the same as the distance between the corresponding points on the image;

Therefore;

ΔABC is congruent to ΔRST by Side-Side-Side SSS, rule of congruency, such that we have;

AB ≅ RS, BC ≅ ST, and AC ≅ RT

m∠BAC ≅ m∠SRT

m∠BCA ≅ m∠STR

m∠BAC ≅ m∠SRT

Therefore;

The true statements are;

• AB = RS

• ΔABC ≅ ΔRST

Therefore;

• m∠BAC ≅ m∠SRT given that ΔABC ≅ ΔRST

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