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 \\( x \\)-axis. describe the sequence of rigid motions. what is nikols likely error?

what is nikols likely error?
\\( \bigcirc \\) a. she did not move the correct units down.
\\( \bigcirc \\) b. she reflected the triangle across the wrong axis.
\\( \bigcirc \\) c. she did not move the correct units to the left.

which of the following is the description of the rigid motions which maps \\( \triangle efg \\) to \\( \triangle mno \\)?
\\( \bigcirc \\) a. a translation 4 units to the left and 4 units down, followed by a reflection across the \\( y \\)-axis
\\( \bigcirc \\) b. a translation 5 units to the left and 5 units down, followed by a reflection across the \\( y \\)-axis
\\( \bigcirc \\) c. a translation 5 units to the left and 5 units down, followed by a reflection across the \\( x \\)-axis

Explanation:

Step1: Analyze translation

For \(E(5,5)\) to \(M(0,0)\):

• \(x\) - coordinate: \(5 - 5=0\) (5 units to the left)
• \(y\) - coordinate: \(5 - 5 = 0\) (5 units down)

For \(F(9,5)\) to \(N(- 4,0)\):

• \(x\) - coordinate: \(9-13=-4\) (Wrong, should be \(9 - 5=4\) but wait, no. Wait \(E(5,5)\) to \(M(0,0)\): \(x\) change \(5 - 0=5\) (left), \(y\) change \(5-0 = 5\) (down). For \(G(5,10)\) to \(O(0,5)\): \(x\) change \(5 - 0=5\) (left), \(y\) change \(10 - 5=5\) (down)

Step2: Analyze reflection

After translation \((x,y)\to(x - 5,y - 5)\). Then reflection across \(x\) - axis: \((x,y)\to(x,-y)\)

For the error part:

• Original translation: from \(E(5,5)\) to \(M(0,0)\) is 5 units left and 5 units down. She said 4 units down.

Answer:

First part: B. A translation 5 units to the left and 5 units down, followed by a reflection across the \(x\) - axis
Second part: A. She did not move the correct units down.