Question

the line segment ab is shown.
if line segment ab were translated 2 units down and 3 units to the right to create line segment ab, what would the end points of the new line segment be?
a. (2,5) and (-6,3)
b. (1,4) and (-7,4)
c. (-2,5) and (6,-3)

Explanation:

Step1: Find the coordinates of points A and B

From the graph, the coordinates of point \(A\) are \((- 2,6)\) and the coordinates of point \(B\) are \((3,-2)\)

Step2: Apply the translation rule

The translation rule is \((x,y)\to(x + 3,y-2)\)
For point \(A(-2,6)\):
\(x=-2+3 = 1\), \(y=6 - 2=4\), so \(A'\) is \((1,4)\)
For point \(B(3,-2)\):
\(x=3+3=6\), \(y=-2-2=-4\)

Answer:

None of the options A, B, C are correct. The endpoints of the new line - segment \(A'B'\) are \((1,4)\) and \((6,-4)\)