Question

question 5
1 pts
which of the following is the correct mapping for shape a to shape b?
options:
$(x,y) \to (x - 7, -y)$
$(x,y) \to (x, y - 4)$
$(x,y) \to (-x, -y)$
$(x,y) \to (-x, y)$

Explanation:

Step1: Analyze symmetry

Observe the positions of shape A (left) and shape B (right). They are symmetric about the y - axis.

Step2: Recall transformation for y - axis symmetry

The transformation for a point \((x,y)\) to be symmetric about the y - axis is \((x,y)\to(-x,y)\). Let's check the other options:

• For \((x,y)\to(x - 7,-y)\): This is a translation left by 7 units and a reflection over the x - axis, which does not match the symmetry.
• For \((x,y)\to(x,y - 4)\): This is a translation down by 4 units, which is not the case here.
• For \((x,y)\to(-x,-y)\): This is a reflection over the origin, which is not the symmetry we see (the y - coordinates remain the same, x - coordinates are negated).

Answer:

\((x,y)\to(-x,y)\) (the last option among the given options)