Question
Triangle PQR is transformed to similar triangle P′Q′R′:
A coordinate plane is shown. Triangle PQR has vertices P at negative 6 comma 6, Q at negative 6 comma 3, and R at negative 3 comma 3. Triangle P prime Q prime R prime has vertices at P prime negative 2 comma 2, Q prime at negative 2 comma 1, and R prime at negative 1 comma 1.
What is the scale factor of dilation? (4 points)
1 over 2
1 over 3
1 over 4
1 over 5
A coordinate plane is shown. Triangle PQR has vertices P at negative 6 comma 6, Q at negative 6 comma 3, and R at negative 3 comma 3. Triangle P prime Q prime R prime has vertices at P prime negative 2 comma 2, Q prime at negative 2 comma 1, and R prime at negative 1 comma 1.
What is the scale factor of dilation? (4 points)
1 over 2
1 over 3
1 over 4
1 over 5
Answers
GPT 3.5
To find the scale factor of dilation, we can compare the corresponding sides of the two triangles and determine their ratios.
The length of side PQ in triangle PQR is 6 - 3 = 3.
The length of side P'Q' in triangle P'Q'R' is 2 - 1 = 1.
Therefore, the ratio of the length of side PQ to the length of side P'Q' is 3/1 = 3.
The scale factor of dilation is the reciprocal of this ratio, so it is 1/3.
Therefore, the scale factor of dilation is 1/3.
The length of side PQ in triangle PQR is 6 - 3 = 3.
The length of side P'Q' in triangle P'Q'R' is 2 - 1 = 1.
Therefore, the ratio of the length of side PQ to the length of side P'Q' is 3/1 = 3.
The scale factor of dilation is the reciprocal of this ratio, so it is 1/3.
Therefore, the scale factor of dilation is 1/3.