Question
Dianna draws triangle ABC
and translates it along the coordinate grid to produce triangle A′B′C′
. Then, she determines the functions f(x)=x+h
and g(y)=y+k
that describe the translation. What are the values of h and k in these functions?
(1 point)
Responses
h=2
and k=−5
h equals 2 and k equals negative 5
h=8
and k=−5
h equals 8 and k equals negative 5
h=5
and k=−8
h equals 5 and k equals negative 8
h=−8
and k=−5
h equals negative 8 and k equals negative 5
and translates it along the coordinate grid to produce triangle A′B′C′
. Then, she determines the functions f(x)=x+h
and g(y)=y+k
that describe the translation. What are the values of h and k in these functions?
(1 point)
Responses
h=2
and k=−5
h equals 2 and k equals negative 5
h=8
and k=−5
h equals 8 and k equals negative 5
h=5
and k=−8
h equals 5 and k equals negative 8
h=−8
and k=−5
h equals negative 8 and k equals negative 5
Answers
GPT-4o mini
To determine the values of \( h \) and \( k \) which describe the translation from triangle \( ABC \) to triangle \( A'B'C' \), we need to know the specific coordinates of the points in triangles \( ABC \) and \( A'B'C' \).
The functions \( f(x) = x + h \) and \( g(y) = y + k \) indicate that the triangle is being translated right by \( h \) units and up by \( k \) units. Thus, \( h \) denotes the horizontal shift and \( k \) denotes the vertical shift.
To choose the correct response from the provided options, you would compare the x-coordinates and y-coordinates of the original and translated points:
- If the x-coordinate of a point in triangle \( ABC \) increases by \( h \) to reach triangle \( A'B'C' \), then \( h \) is positive if the point moves rightward, and negative if it moves leftward.
- Similarly, if the y-coordinate increases by \( k \) to reach the new position, \( k \) is positive for upward movement and negative for downward movement.
Without specific points given in the question, I cannot provide you with the precise values of \( h \) and \( k \). However, you can determine these values by measuring the changes in the coordinates of points from triangle \( ABC \) to triangle \( A'B'C' \).
If you have the coordinates for triangle \( ABC \) and its translated version \( A'B'C' \), you can calculate \( h \) and \( k \) and select the correct answer from the options provided. Please provide the coordinates if available, and I can help you calculate \( h \) and \( k \).
The functions \( f(x) = x + h \) and \( g(y) = y + k \) indicate that the triangle is being translated right by \( h \) units and up by \( k \) units. Thus, \( h \) denotes the horizontal shift and \( k \) denotes the vertical shift.
To choose the correct response from the provided options, you would compare the x-coordinates and y-coordinates of the original and translated points:
- If the x-coordinate of a point in triangle \( ABC \) increases by \( h \) to reach triangle \( A'B'C' \), then \( h \) is positive if the point moves rightward, and negative if it moves leftward.
- Similarly, if the y-coordinate increases by \( k \) to reach the new position, \( k \) is positive for upward movement and negative for downward movement.
Without specific points given in the question, I cannot provide you with the precise values of \( h \) and \( k \). However, you can determine these values by measuring the changes in the coordinates of points from triangle \( ABC \) to triangle \( A'B'C' \).
If you have the coordinates for triangle \( ABC \) and its translated version \( A'B'C' \), you can calculate \( h \) and \( k \) and select the correct answer from the options provided. Please provide the coordinates if available, and I can help you calculate \( h \) and \( k \).