Question

figure jklmn is reflected across the x - axis to form figure jklmn. tell whether each statement is true or false. a. l is located at (-3,4). b. m is located 1 unit below the x - axis. c. the y - coordinate of k is the opposite of the y - coordinate of k. d. the line of reflection is the y - axis. e. nm = nm. f. the x - coordinate of n is the opposite of the x - coordinate of n. g. m∠j = m∠j

Explanation:

Step1: Recall reflection rule across x - axis

When a point $(x,y)$ is reflected across the x - axis, the new point is $(x, - y)$.

Step2: Analyze statement a

Assume the original coordinates of $L$ are $(x,y)$. After reflection across the x - axis, $L'$ has coordinates $(x,-y)$. Without seeing the original coordinates of $L$ precisely from the graph, we note that reflection across x - axis changes the sign of the y - coordinate. If we assume original $L$ has positive y - coordinate, $L'$ will have negative y - coordinate. So this statement is False.

Step3: Analyze statement b

Let's assume the original coordinates of $M$ are $(x,y)$. After reflection across the x - axis, $M'=(x, - y)$. If we assume original $M$ has $y = 1$, after reflection $M'$ has $y=-1$ which is 1 unit below the x - axis. But we need to check from the graph. If we assume original $M$ has positive y - coordinate, after reflection it will be negative. If the original $y$ value of $M$ is 1, then $M'$ is 1 unit below the x - axis. So this statement is True.

Step4: Analyze statement c

By the rule of reflection across the x - axis $(x,y)\to(x, - y)$. For point $K$, if its original coordinates are $(x_K,y_K)$, then $K'$ has coordinates $(x_K,-y_K)$. So the y - coordinate of $K'$ is the opposite of the y - coordinate of $K$. This statement is True.

Step5: Analyze statement d

The problem states that the figure is reflected across the x - axis, not the y - axis. So this statement is False.

Step6: Analyze statement e

Reflection is a rigid transformation, which preserves distances. So the length of a line - segment before and after reflection is the same. That is, $N'M'=NM$. This statement is True.

Step7: Analyze statement f

Reflection across the x - axis changes the sign of the y - coordinate, not the x - coordinate. So the x - coordinate of $N'$ is the same as the x - coordinate of $N$. This statement is False.

Step8: Analyze statement g

Reflection is a rigid transformation that preserves angle measures. So $m\angle J'=m\angle J$. This statement is True.

Answer:

a. False
b. True
c. True
d. False
e. True
f. False
g. True