Question

Tamika is trying to dilate a triangle drawn on a coordinate plane using a magnitude of 4 with reference to the origin. If the original triangle has vertices at coordinate points (12,0) , (5,0) , and (4,3) , what are the coordinate points of the new vertices of the dilated triangle?(1 point) Responses (18,0) , (54,0) , and (1,34) left parenthesis Start Fraction 1 over 8 End Fraction comma 0 right parenthesis , left parenthesis Start Fraction 5 over 4 End Fraction comma 0 right parenthesis , and left parenthesis 1 comma Start Fraction 3 over 4 End Fraction right parenthesis (92,4) , (9,4) , and (8,7) left parenthesis Start Fraction 9 over 2 End Fraction comma 4 right parenthesis , left parenthesis 9 comma 4 right parenthesis , and left parenthesis 8 comma 7 right parenthesis (−72,−4) , (1,−4) , and (0,−1) left parenthesis negative Start Fraction 7 over 2 End Fraction comma negative 4 right parenthesis , left parenthesis 1 comma negative 4 right parenthesis , and left parenthesis 0 comma negative 1 right parenthesis (2,0) , (20,0) , and (16,12)

Answer 1

To dilate a triangle around the origin (0, 0) by a scale factor of 4, you multiply each of the triangle's vertices by the scale factor.

The original vertices of the triangle are:

• A (12, 0)
• B (5, 0)
• C (4, 3)

Now, let's perform the dilation for each vertex:

1. For vertex A (12, 0): \( A' = (12 \times 4, 0 \times 4) = (48, 0) \)

2. For vertex B (5, 0): \( B' = (5 \times 4, 0 \times 4) = (20, 0) \)

3. For vertex C (4, 3): \( C' = (4 \times 4, 3 \times 4) = (16, 12) \)

Thus, the new vertices of the dilated triangle are:

• A' (48, 0)
• B' (20, 0)
• C' (16, 12)

Now let’s see if this matches any of the provided responses:

• (18,0), (54,0), and (1,34)
• (92,4), (9,4), and (8,7)
• (−72,−4), (1,−4), and (0,−1)
• (2,0), (20,0), and (16,12)

The correct vertices after dilation are (48, 0), (20, 0), and (16, 12). However, none of the provided options match the calculated results precisely.

It seems that the correct answer based on the calculations for the dilation of triangle vertices does not match any option exactly. The closest match concerning two vertices is (20, 0) and (16, 12), but the third vertex was miscalculated in the options provided. Please double-check the question's options and confirm whether any typographical error exists.