Question

If triangle XYZ is reflected across the line y = 1 to create triangle X'Y'Z', what is the ordered pair of X'?

Ordered Points Location:
Point X: (3,-1)
Point Y: (4,-4)
Point Z: (1,-2)

Answers:
A) (3,3)
B) (3,1)
C) (-1,-1)
D) (-3,-1)

Answer 1

X' would be located at (3,3) after a reflection across y = 1.

The y value of the ordered pair is currently 2 units away from the line of reflection. Once reflected, it must be 2 units away but on the other side of the line of reflection.

Answer 2

Answer: The ordered pair of X' is (A) (3, 3).

Step-by-step explanation: Given that the triangle XYZ is reflected across the line y = 1 to create triangle X'Y'Z'.

The co-ordinates of the vertices of ΔXYZ are X(3, -1), Y(4, -4) and Z(1, -2).

We are to find the ordered pair of X'.

The triangle XYZ and its reflection X'Y'Z' across the line y = 1 is shown in the attached figure.

Since the triangle XYZ is reflected across Y-axis, so the x-co-ordinate of each vertex will remain same.

So, the x-co-ordinate of X' is 3, because x-co-ordinate of X is 3.

Now, to find the y-co-ordinate, first we will find the distance between the point X and the line of reflection y = 2.

The distance between X(3, -1) and y = 1 is (1 + 1)=2 units. This is same as the distance between the line of reflection and the image X'.

Therefore, the co-ordinates of X' are (3, -1+2+2)=(3, 3).

Thus, (A) is the correct option.