Question

question 4 (3 points) triangle abc has coordinates of a(4, 3), b(-2, 4), and c(1, -5). find the coordinates of triangle abc after a translation of 5 units to the left and 3 units up. a(), b(), c() blank 1: blank 2: blank 3: blank 4: blank 5: blank 6:

Explanation:

Step1: Recall translation rules

For a translation of \( h \) units left/right and \( k \) units up/down, the new coordinates \((x', y')\) of a point \((x, y)\) are given by \( x' = x - h \) (left) or \( x' = x + h \) (right), and \( y' = y + k \) (up) or \( y' = y - k \) (down). Here, \( h = 5 \) (left) and \( k = 3 \) (up).

Step2: Find \( A' \) coordinates

Given \( A(4, 3) \), apply the translation:
\( x' = 4 - 5 = -1 \)
\( y' = 3 + 3 = 6 \)
So \( A'(-1, 6) \)

Step3: Find \( B' \) coordinates

Given \( B(-2, 4) \), apply the translation:
\( x' = -2 - 5 = -7 \)
\( y' = 4 + 3 = 7 \)
So \( B'(-7, 7) \)

Step4: Find \( C' \) coordinates

Given \( C(1, -5) \), apply the translation:
\( x' = 1 - 5 = -4 \)
\( y' = -5 + 3 = -2 \)
So \( C'(-4, -2) \)

Answer:

\( A'(-1, 6) \), \( B'(-7, 7) \), \( C'(-4, -2) \)