In the figure shown, triangle RST undergoes reflections across two line. R''S''T’’ is the final image of RST Triangle RST is first reflected across the line x=0 and then across line
a. x=0
b. y=0
c. y=x
d. y=-x

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Explanation:

Point T is at (-2,1)

When we reflect it over the line x = 0, aka the y axis, we use the rule so T(-2,1) becomes T ' (2, 1). The x coordinate flipped in sign, while the y coordinate stays the same.

Then the final transformation is reflecting over y = -x using the rule . Therefore, the point (2,1) moves to (-1, -2) which is where T'' is located in the diagram.

You apply the same two transformations for the points R and S to get R'' and S'' respectively.

Note: A composition of two reflections, where the lines of reflection aren't parallel, form a rotation. In this case, we have a 90 degree counterclockwise rotation when going from triangle RST to triangle R''S''T''.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.