Question

figure jkl mn is reflected across the y - axis to form figure jklmn. part a draw figure jklmn. what are the coordinates of the vertices of figure jklmn? solution part b decide if each statement describing figures jkl mn and jklmn is true or false. choose true or false for each statement. a. l is located at (-3,4). b. m is located 4 units left of the y - axis. c. the y - coordinate of n is the opposite of the y - coordinate of n. d. jk = jk e. m is located at (-4,1).

Explanation:

Step1: Recall reflection rule

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

Step2: Find coordinates of vertices of $J'K'L'M'N'$

Assume the coordinates of $J(x_J,y_J)$, $K(x_K,y_K)$, $L(x_L,y_L)$, $M(x_M,y_M)$, $N(x_N,y_N)$ in figure $JKLMN$. After reflection across the y - axis, the coordinates of $J'$ is $(-x_J,y_J)$, $K'$ is $(-x_K,y_K)$, $L'$ is $(-x_L,y_L)$, $M'$ is $(-x_M,y_M)$, $N'$ is $(-x_N,y_N)$.

Step3: Analyze statements in Part B

Statement a

If the original coordinates of $L$ is $(3,4)$, after reflection across the y - axis, $L'$ is $(- 3,4)$. So this statement is True.

Statement b

If the original coordinates of $M$ is $(4,1)$, after reflection across the y - axis, $M'$ is $(-4,1)$ which is 4 units left of the y - axis. So this statement is True.

Statement c

When reflecting a point across the y - axis, the y - coordinate remains the same. So the y - coordinate of $N'$ is the same as the y - coordinate of $N$, and this statement is False.

Statement d

Reflection is a rigid transformation, which preserves distance. So $J'K'=JK$. This statement is True.

Statement e

If the original coordinates of $M$ is $(4,1)$, after reflection across the y - axis, $M'$ is $(-4,1)$. This statement is True.

Answer:

Part A

(The drawing of the figure should be done by reversing the x - coordinates of the vertices of $JKLMN$ while keeping the y - coordinates the same). Coordinates of vertices are found by applying the rule $(x,y)\to(-x,y)$ to each vertex of $JKLMN$.

Part B

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