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)

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.  

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

chiken

step-by-step explanation: