Question

what are the image coordinates after the figure has been translated +2 units vertically and -4 units horizontally and then reflected over the x - axis? a(-3,7) b(0,4) c(-3,2) a(-3,-7) b(0,-4) c(-3,-2) a(1,-5) b(4,-2) c(1,0) a(3,1) b(6,-2) c(3,-4)

Explanation:

Step1: Find original coordinates

Assume original coordinates \(A(1,5)\), \(B(4,2)\), \(C(1,0)\) (estimated from the graph).

Step2: Translate coordinates

For a point \((x,y)\), vertical translation \(+ 2\) (add \(2\) to \(y\)) and horizontal translation \(-4\) (subtract \(4\) from \(x\)).
For \(A(1,5)\): \(x = 1-4=-3\), \(y = 5 + 2=7\) → \((-3,7)\)
For \(B(4,2)\): \(x = 4-4 = 0\), \(y=2 + 2=4\) → \((0,4)\)
For \(C(1,0)\): \(x = 1-4=-3\), \(y=0 + 2=2\) → \((-3,2)\)

Step3: Reflect over \(x -\)axis

When reflecting a point \((x,y)\) over the \(x -\)axis, the rule is \((x,-y)\)
For \((-3,7)\): \((-3,-7)\)
For \((0,4)\): \((0,-4)\)
For \((-3,2)\): \((-3,-2)\)

Answer:

B. \(A'(-3,-7)\), \(B'(0,-4)\), \(C'(-3,-2)\)