Question

given points j(3,5), a(7,6), and r(5,2), graph δjar and its reflection image across the given line. ( r_{x\text{-axis}} ) choose the correct graph below. a. b. c. d. (images of graphs)

Explanation:

Step1: Recall Reflection Rule

To reflect a point \((x,y)\) across the \(x\)-axis, the rule is \((x,y)\to(x, -y)\).

Step2: Find Reflected Points

• For \(J(3,5)\): Apply the rule, new point \(J'(3, - 5)\).
• For \(A(7,6)\): Apply the rule, new point \(A'(7, - 6)\).
• For \(R(5,2)\): Apply the rule, new point \(R'(5, - 2)\).

Step3: Match with Graphs

Now we check the graphs. The original triangle has points \(J(3,5)\), \(A(7,6)\), \(R(5,2)\). The reflected points should have the same \(x\)-coordinates and \(y\)-coordinates negated. Looking at the options, in option A, the reflected triangle (blue) has points that match the reflection rule: \(J'\) should be \((3, - 5)\), \(A'\) \((7, - 6)\), \(R'\) \((5, - 2)\). Let's check the coordinates in the graphs. In option A, the blue triangle's vertices seem to correspond to these reflected coordinates. Other options have incorrect coordinates for the reflected points. For example, option B has incorrect \(x\) or \(y\) coordinates, option C and D also don't match the reflection rule.

Answer:

A