Question

question 3 the figures below are congruent. find \b.\ 8.g.2 question 4 which series of transformations demonstrates that the figures are congruent? 8.g.2 a) a reflection over the x axis followed by a reflection over the y axis b) a translation 2 units down followed by a reflection over the x axis c) a rotation of 90° clockwise about the origin followed by a reflection over the x axis d) a translation 3 units left followed by a reflection over the x axis answer: _ © classroom 127

Explanation:

Step1: Use the property of congruent figures

Congruent figures have equal corresponding sides. In the first figure, the side parallel to the side labeled \(B\) in the second figure has a length of \(3\). So \(B = 3\).

Step2: Analyze the transformations for congruence

• For option a: A reflection over the \(x\)-axis followed by a reflection over the \(y\)-axis. Let's assume a point \((x,y)\) on the original figure. After reflection over the \(x\)-axis, it becomes \((x, - y)\), and after reflection over the \(y\)-axis, it becomes \((-x,-y)\).
• For option b: A translation \(2\) units down changes the \(y\)-coordinate \((x,y)\to(x,y - 2)\), then a reflection over the \(x\)-axis \((x,y-2)\to(x,2 - y)\) which does not map the figure correctly.
• For option c: A rotation of \(90^{\circ}\) clockwise about the origin \((x,y)\to(y,-x)\), then a reflection over the \(x\)-axis \((y,-x)\to(y,x)\) which is not the correct transformation.
• For option d: A translation \(3\) units left \((x,y)\to(x - 3,y)\), then a reflection over the \(x\)-axis \((x-3,y)\to(x - 3,-y)\) which is not the correct transformation.

The correct transformation is a reflection over the \(x\)-axis followed by a reflection over the \(y\)-axis.

Answer:

For the first part (finding \(B\)): \(B = 3\). For the second part (transformation): a) A reflection over the \(x\) - axis followed by a reflection over the \(y\) - axis.