Question

1. point $(2,5)$ is a vertex of an object on a coordinate plane. the object is reflected over the line $y = x$, and then rotated $90^{circ}$ clockwise around the origin. what is the coordinate of the point after the sequence of transformations? reflection $\to(square,square)$ rotation $\to(square,square)$ 2. quadrilateral $pkrh$ is shown on a coordinate grid. what is the value of point $k$ after a $180^{circ}$ clockwise rotation around the origin is performed on the quadrilateral? after rotation $k=(square,square)$

Explanation:

Step1: Reflection over \(y = x\)

When a point \((a,b)\) is reflected over the line \(y=x\), the rule is \((a,b)\to(b,a)\). For the point \((2,5)\), after reflection over \(y = x\), we get \((5,2)\).

Step2: \(90^{\circ}\) clockwise rotation

The rule for a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y,-x)\). Using the point \((5,2)\) from the reflection step, we substitute \(x = 5\) and \(y=2\) into the rotation rule. So, \((5,2)\to(2,- 5)\)

For the second problem (assuming we can find the coordinates of \(K\) from the grid, let's say \(K=(x,y)\)):

Step1: \(180^{\circ}\) clockwise rotation

The rule for a \(180^{\circ}\) clockwise rotation about the origin is \((x,y)\to(-x,-y)\)

Answer:

1. Reflection: \((5,2)\)

Rotation: \((2,-5)\)

1. (Assuming \(K=(x,y)\) from the grid) After rotation \(K=(-x,-y)\) (you need to substitute the actual \(x\) and \(y\) values of point \(K\) from the grid into \((-x,-y)\))