Question

the coordinates of the vertices of parallelogram rstu are r(0,0), s(2,3), t(6,3), and u(4,0). what are the coordinates of the vertices when reflected across the line y = x?

Explanation:

Step1: Recall the reflection rule

When a point \((x,y)\) is reflected across the line \(y = x\), the new coordinates are \((y,x)\).

Step2: Apply the rule to each vertex

• For \(R(0,0)\):

Using the rule \((x,y)\to(y,x)\), we get \(R'(0,0)\) since \(x = 0,y=0\) and \(y,x\) is also \(0,0\).

• For \(S(2,3)\):

Here \(x = 2,y = 3\). After reflection across \(y=x\), the coordinates become \(S'(3,2)\) (because we swap \(x\) and \(y\) values).

• For \(T(6,3)\):

Since \(x = 6,y = 3\), after reflection across \(y=x\), the coordinates are \(T'(3,6)\) (swap \(x\) and \(y\) values).

• For \(U(4,0)\):

Given \(x = 4,y = 0\), after reflection across \(y=x\), the coordinates are \(U'(0,4)\) (swap \(x\) and \(y\) values).

Answer:

\(R'(0,0)\), \(S'(3,2)\), \(T'(3,6)\), \(U'(0,4)\)