Question

triangle def has coordinates d(4, -1), e(5, 2), and f(1, 2). determine the coordinates of the vertices of the image after a translation along the vector <1, 0>.
a) d(4, 1), e(5, -2), and f(1, -2)
b) d(-4, -1), e(-5, 2), and f(-1, 2)
c) d(5, -1), e(6, 2), and f(2, 2)
d) d(1, 0), e(2, 3), and f(-2, 3)

Explanation:

Step1: Apply translation rule

For a translation vector \(\langle a,b
angle\), the rule is \((x,y)\to(x + a,y + b)\). Here \(a = 1\), \(b=0\).
For point \(D(4,-1)\): \(x=4\), \(y = - 1\). New \(x\) - coordinate \(x'=4 + 1=5\), new \(y\) - coordinate \(y'=-1+0=-1\). So \(D'\) is \((5,-1)\).

Step2: Translate point \(E\)

For point \(E(5,2)\): \(x = 5\), \(y = 2\). New \(x\) - coordinate \(x'=5 + 1=6\), new \(y\) - coordinate \(y'=2+0=2\). So \(E'\) is \((6,2)\).

Step3: Translate point \(F\)

For point \(F(1,2)\): \(x = 1\), \(y = 2\). New \(x\) - coordinate \(x'=1 + 1=2\), new \(y\) - coordinate \(y'=2+0=2\). So \(F'\) is \((2,2)\).

Answer:

C. \(D'(5,-1)\), \(E'(6,2)\), and \(F'(2,2)\)