Question

triangle abc has vertices a(4, 5), b(0, 5), and c(3, −1). the triangle is translated 3 units to the left and 1 unit up. what are the coordinates of b after the translation? (1, 6) (-3, 6) (0, 0) (3, 1)

Explanation:

Step1: Recall translation rules

For a point \((x,y)\), translating \(a\) units left means subtracting \(a\) from the \(x\)-coordinate, and translating \(b\) units up means adding \(b\) to the \(y\)-coordinate. So the translation rule is \((x,y)\to(x - 3,y + 1)\) (since 3 units left and 1 unit up).

Step2: Apply rule to point B

The coordinates of point \(B\) are \((0,5)\). Using the translation rule:

• New \(x\)-coordinate: \(0-3=-3\)
• New \(y\)-coordinate: \(5 + 1=6\)

So the coordinates of \(B'\) are \((-3,6)\).

Answer:

B. \((-3, 6)\)