Quadrilateral RAPS is located at the vertices R(-4,1), A(-3, 4), P(0,5), S(-1,1). Where will points

R", A", P", S", be located after the quadrilateral has been reflected

across the line y - x and then rotated 180° about the origin?

R''(-1, 4), A''(-4, 3), P''(-5, 0), S''(-1, 1)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new position. Types of transformation include dilation, reflection, translation and rotation.

If a point A(x, y) is reflected over the line y = x, the new point is at  A'(y, x)

If a point A(x, y) is  rotated 180° clockwise about the origin, the new location is at A'(-x, -y)

Since Quadrilateral RAPS is located at the vertices  R(-4,1), A(-3, 4), P(0,5), S(-1,1), After been reflected  across the line y = x, the new locations are at:

R'(1, -4), A'(4, -3), P'(5, 0), S'(1, -1)

Then the rotation of the points R'(1, -4), A'(4, -3), P'(5, 0), S'(1, -1) 180° about the origin gives:

R''(-1, 4), A''(-4, 3), P''(-5, 0), S''(-1, 1)