Question

refer to the graph.
which set of coordinates models the image of the triangle after a translation along < 2, -9 > ?
a) m(-5, 16), n(-2, 13), p(0, 15)
b) m(-1, -2), n(2, -5), p(4, -3)
c) m(-5, -2), n(-2, -5), p(0, -3)
d) m(-1, 16), n(2, 13), p(4, 15)

Explanation:

Step1: Recall Translation Rule

For a translation vector \(\langle a, b
angle\), the new coordinates \((x', y')\) of a point \((x, y)\) are given by \(x' = x + a\) and \(y' = y + b\). Here, \(a = 2\) and \(b=-9\).

Step2: Translate Point M(-3,7)

For \(M(-3, 7)\):
\(x' = -3 + 2 = -1\)
\(y' = 7 + (-9) = -2\)
So, \(M'(-1, -2)\)

Step3: Translate Point N(0,4)

For \(N(0, 4)\):
\(x' = 0 + 2 = 2\)
\(y' = 4 + (-9) = -5\)
So, \(N'(2, -5)\)

Step4: Translate Point P(2,6)

For \(P(2, 6)\):
\(x' = 2 + 2 = 4\)
\(y' = 6 + (-9) = -3\)
So, \(P'(4, -3)\)

Answer:

B) \(M'(-1, -2)\), \(N'(2, -5)\), \(P'(4, -3)\)