Question

Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. Which equation explains the relationship between segment AB and segment A double prime B double prime? coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3 segment A double prime B double prime = segment AB over 2 segment AB = segment A double prime B double prime over 2 segment AB over segment A double prime B double prime = one half segment A double prime B double prime over segment AB = 2

Answer 1

Answer: The answer is A

Explanation:

Answer 2

• A. segment A double prime B double prime = segment AB over 2

Explanation:

Triangle ABC with coordinates of:

• A = (-3, 3), B = (1, -3), C = (-3, -3)

Translation (x + 2, y + 0), coordinates will be:

• A' = (-1, 3), B = ( 3, -3), C = (-1, -3)

Dilation by a scale factor of 1/2 from the origin, coordinates will be:

• A'' = (-0.5, 1.5), B'' = (1.5, -1.5), C= (-0.5, -1.5)

Let's find the length of AB and A''B'' using distance formula

• d = √(x2-x1)² + (y2 - y1)²

• AB = √(1-(-3))² + (-3 -3)² = √4²+6² = √16+36 = √52 = 2√13
• A''B'' = √(1.5 - (-0.5)) + (-1.5 - 1.5)² = √2²+3² = √13

We see that

• AB = 2A''B''

Now the answer options:

A. segment A double prime B double prime = segment AB over 2

• Correct

B. segment AB = segment A double prime B double prime over 2

• Incorrect. Should be AB = A''B''*2

C. segment AB over segment A double prime B double prime = one half

• Incorrect. Should be AB/A''B'' = 2

D. segment A double prime B double prime over segment AB = 2

• Incorrect. Should be A''B''/AB = 1/2