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 changes \(x\) to \(x - a\), and translating \(b\) units up changes \(y\) to \(y + b\). Here, \(a = 3\) (left) and \(b = 1\) (up), and the original point \(B\) is \((0, 5)\).

Step2: Apply x - coordinate translation

The original \(x\) - coordinate of \(B\) is \(0\). After translating 3 units left, the new \(x\) - coordinate is \(0-3=-3\).

Step3: Apply y - coordinate translation

The original \(y\) - coordinate of \(B\) is \(5\). After translating 1 unit up, the new \(y\) - coordinate is \(5 + 1=6\).

Answer:

\((-3, 6)\)