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

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

Accepted Answer

# 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.

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze translation

Step2: Analyze reflection

Answer: