Question

Use the image to answer the question.

A coordinate plane shows two plotted triangles upper A upper B upper C, and upper A prime upper B prime upper C prime, in the same orientation. Both axes range from negative 7 to 7 in increments of 1.

Mel draws triangle ABC
and translates it along the coordinate grid to produce triangle A′B′C′
. Then, he 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=1
and k=6
h equals 1 and k equals 6

h=6
and k=−1
h equals 6 and k equals negative 1

h=−1
and k=−6
h equals negative 1 and k equals negative 6

h=−1
and k=6

Answer 1

To determine the values of \( h \) and \( k \) in the functions \( f(x) = x + h \) and \( g(y) = y + k \) that describe the translation from triangle ABC to triangle A'B'C', we need to look at the transformation that was applied to the coordinates of the triangles.

The translation function suggests that the triangle is moved \( h \) units horizontally (left or right) and \( k \) units vertically (up or down).

Without the specific coordinates of the points of triangles ABC and A'B'C', I cannot calculate the exact values of \( h \) and \( k \) directly from the image. However, the process to find \( h \) and \( k \) is as follows:

1. Identify the coordinates of a point from triangle ABC (e.g., point A) and the corresponding point from triangle A'B'C' (e.g., point A').
2. Calculate the horizontal shift \( h = x' - x \) where \( (x, y) \) are the coordinates of point A and \( (x', y') \) are the coordinates of point A'.
3. Calculate the vertical shift \( k = y' - y \).
4. Compare the calculated values with the provided options.

If you can provide the coordinates or information about the relative positions of the triangles, I can help you determine the values of \( h \) and \( k \) more precisely.