Question

which coordinate is the same as the x - coordinate of point ( a )?
y - coordinate of point ( a )
which coordinate is the same as the y - coordinate of point ( a )?
opposite of x - coordinate of point ( a )
( \begin{array}{|c|c|}hline \triangle abc&\triangle abc\hline a(-1,2)&a(2,1)\hline b(-4,3)&b(3,4)\hline c(-3,1)&c(1,3)\hlineend{array} )
( 90^{circ} ) clockwise rotation:
( (x,y)\to(y,-x) )

Explanation:

Step1: Identify the \(x\)-coordinate of \(A'\)

The coordinates of \(A'\) are \((2,1)\). The \(x\)-coordinate of \(A'\) is \(2\).

Step2: Identify the \(y\)-coordinate of \(A\)

The coordinates of \(A\) are \((-1,2)\). The \(y\)-coordinate of \(A\) is \(2\).

Step3: Identify the \(y\)-coordinate of \(A'\)

The coordinates of \(A'\) are \((2,1)\). The \(y\)-coordinate of \(A'\) is \(1\).

Step4: Identify the opposite of the \(x\)-coordinate of \(A\)

The \(x\)-coordinate of \(A\) is \(-1\). The opposite of \(-1\) is \(1\).

Answer:

The \(x\)-coordinate of \(A'\) (\(2\)) is the same as the \(y\)-coordinate of \(A\) (\(2\)). The \(y\)-coordinate of \(A'\) (\(1\)) is the same as the opposite of the \(x\)-coordinate of \(A\) (opposite of \(-1\) is \(1\)).