Question

determine the coordinates of the image following each given translation. a. triangle abc with coordinates a(2, 4), b(3, 6), and c(5, 1) is translated 4 units horizontally. b. parallelogram defg with coordinates d(0, 2), e(1, 5), f(6, 5), and g(5, 2) is translated - 7 units horizontally. fill in the blank 2 points fill in the blank 2 points

Explanation:

Step1: Recall translation rule for horizontal shift

For a horizontal translation of \(h\) units, if \(h>0\) the point \((x,y)\) moves to \((x + h,y)\) and if \(h<0\) the point \((x,y)\) moves to \((x+h,y)\). Here, for a 4 - unit horizontal translation, we add 4 to the \(x\) - coordinate of each point.

Step2: Calculate new coordinates of point A

Given \(A(2,4)\), new \(x\) - coordinate is \(2 + 4=6\), \(y\) - coordinate remains the same. So \(A'(6,4)\).

Step3: Calculate new coordinates of point B

Given \(B(3,6)\), new \(x\) - coordinate is \(3 + 4 = 7\), \(y\) - coordinate remains the same. So \(B'(7,6)\).

Step4: Calculate new coordinates of point C

Given \(C(5,1)\), new \(x\) - coordinate is \(5+4 = 9\), \(y\) - coordinate remains the same. So \(C'(9,1)\).

Answer:

A'(6,4), B'(7,6), C'(9,1)