Question

translating a figure
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

To translate a point \((x, y)\) \(h\) units left and \(k\) units up, the new coordinates are \((x - h, y + k)\). Here, \(h = 3\) (left) and \(k = 1\) (up).

Step2: Identify coordinates of B

The original coordinates of \(B\) are \((0, 5)\).

Step3: Apply translation

For \(x\)-coordinate: \(0 - 3=- 3\)
For \(y\)-coordinate: \(5 + 1 = 6\)
So the coordinates of \(B'\) are \((-3, 6)\).

Answer:

\((-3, 6)\) (corresponding to the option \((-3, 6)\))