Question

triangle abc has coordinates a(2, 0), b(-1, 5), and c(4, 3). determine the coordinates of the vertices of the image after a translation along the vector...
options:
a) a(2, 0), b(-1, -5), and c(4, -3)
b) a(-2, 0), b(1, 5), and c(-4, 3)
c) a(2, 2), b(-1, 7), and c(4, 5)
d) a(5, -4), b(2, 1), and c(7, -1)

Explanation:

Step1: Analyze translation pattern

Assume the translation vector is \((h, k)\). For a point \((x, y)\), the image is \((x + h, y + k)\). Let's check each option by finding \(h\) and \(k\) from point \(A\).

Step2: Check Option C

Original \(A(2, 0)\), image \(A'(2, 2)\). So \(h = 2 - 2 = 0\), \(k = 2 - 0 = 2\).
Check \(B(-1, 5)\): \(-1 + 0 = -1\), \(5 + 2 = 7\) (matches \(B'(-1, 7)\)).
Check \(C(4, 3)\): \(4 + 0 = 4\), \(3 + 2 = 5\) (matches \(C'(4, 5)\)).

Answer:

C. \(A'(2, 2)\), \(B'(-1, 7)\), and \(C'(4, 5)\)