Triangle jkl is transformed by performing a 90 clockwise rotation about the origin and then a reflection over the y-axis, creating triangle j’’k’’l’’. which transformation will map j’’k’’l’’ back to jkl? a: a reflection over the y-axis and then a 90 clockwise rotation about the origin b: a reflection over the x-axis and then a 90 counterclockwise rotation about the origin c: a reflection over the x-axis and then a 90 clockwise rotation about the origin d: a reflection over the x-axis and then a reflection over the y-axis

General Idea:

Reflection Rules:

The reflection of the point (x,y) across the x-axis is the point (x,-y).

The reflection of the point (x,y) across the y-axis is the point (-x,y).

Rotation Rules:

The 90 degree counterclockwise rotation about the origin of a point (x, y) is the point (-y, x)

The 180 degree counterclockwise rotation about the origin of a point (x, y) is the point (-x, -y)

The 270 degree counterclockwise rotation about the origin of a point (x, y) is the point (y, -x)

The 90 degree clockwise rotation about the origin of a point (x, y) is the point (y, -x)

The 180 degree clockwise rotation about the origin of a point (x, y) is the point (-x, -y)

The 270 degree clockwise rotation about the origin of a point (x, y) is the point (-y, x)

Applying the concept:

Let us consider any one of the vertices of the triangle. Let J is given by the point (x, y).

(x, y) becomes (y, -x) after performing a 90 clockwise rotation about the origin and then reflecting that point over the y-axis, we get J'(-y, -x)

We basically need to UNDO what we did to get the point J'(-y, -x) so that we can get it back J(x, y) .

We need to decide on what transformations to be done to J'(-y,-x) so that we get J(x, y)

Conclusion:

If we reflect the point (-y, -x) across the x-axis, then we get (-y, x),

And if we do 90 degree clockwise rotation to the point (-y, x), then we will get back to (x, y)

Option C is the right answer.

The transformation "a reflection over the x-axis and then a 90 clockwise rotation about the origin" will map J'K'L' back to JKL.

70

step-by-step explanation:

2*5=10

4*15=60

60+10=

70