Question

on a math test nikol needs to describe the motions which map (\triangle efg) to (\triangle mno). the coordinates of (\triangle efg) are (e(5,5)), (f(9,5)), and (g(5,10)). the coordinates of (\triangle mno) are (m(0,0)), (n(-4,0)), and (o(0,5)). she says there is a translation 5 units to the left and 5 units down, followed by a reflection across the (y -)axis. describe the sequence of rigid motions. what is nikals likely error? which of the following is the description of the rigid motions which maps (\triangle efg) to (\triangle mno)? a. a translation 4 units to the left and 4 units down, followed by a reflection across the (y -)axis b. a translation 5 units to the left and 5 units down, followed by a reflection across the (y -)axis c. a translation 5 units to the left and 5 units down, followed by a reflection across the (x -)axis

Explanation:

Step1: Analyze the translation part

For the \(x -\)coordinates: \(E(5,5)\) to \(M(0,0)\), \(5 - 0=5\) (left - direction for \(x\) - axis decrease). For the \(y -\)coordinates: \(E(5,5)\) to \(M(0,0)\), \(5-0 = 5\) (down - direction for \(y\) - axis decrease). So the translation is \(5\) units to the left and \(5\) units down.

Step2: Analyze the reflection part

After translation, if we consider the orientation. If we reflect a figure over the \(x -\)axis, the rule is \((x,y)\to(x, - y)\). If we reflect over the \(y -\)axis, the rule is \((x,y)\to(-x,y)\). Let's check the orientation of the triangles. After translation of \(\triangle EFG\) \(5\) units left and \(5\) units down, to match the orientation of \(\triangle MNO\), we need to reflect over the \(y -\)axis.

Answer:

B. A translation 5 units to the left and 5 units down, followed by a reflection across the \(y -\)axis