Question

question
which transformation would take figure a to figure b?

answer attempt 1 out of 2
a clockwise rotation of 270° about the origin a clockwise rotation of 90° about the origin
a reflection over the y - axis a reflection over the x - axis

Explanation:

Step1: Analyze reflection over x - axis

A reflection over the x - axis changes the sign of the y - coordinate of a point \((x,y)\) to \((x, - y)\). Let's take a vertex of Figure A, say if we consider a vertex with coordinates (for example, one of the vertices of A: let's assume a vertex is at \((4,2)\)). After reflection over x - axis, it would be \((4, - 2)\). Looking at Figure B, the corresponding vertex (by shape matching) should have a similar x - coordinate and negative y - coordinate. Let's check the overall shape. The shape of A and B: when we reflect A over the x - axis, the orientation of the shape (the "up" and "down" parts) should flip. Figure A is above the x - axis, Figure B is below the x - axis, and the shape's orientation (the angles and the relative positions of the sides) matches a reflection over the x - axis.

Step2: Analyze other options

• For a reflection over the y - axis: It changes \((x,y)\) to \((-x,y)\). The x - coordinates would be negated, but Figure B does not have negated x - coordinates relative to A (A is in the positive x - region, B is also in positive x - region, just y - coordinates are negative). So reflection over y - axis is incorrect.
• For a clockwise rotation of \(90^{\circ}\) about the origin: The rotation rule for \(90^{\circ}\) clockwise is \((x,y)\to(y, - x)\). The resulting shape would have a different orientation (the sides would be rotated in a way that doesn't match B).
• For a clockwise rotation of \(270^{\circ}\) about the origin: The rotation rule for \(270^{\circ}\) clockwise is \((x,y)\to(-y,x)\), which also would not match the shape of B.

Answer:

A reflection over the x - axis