Question

triangle abc is shown on the coordinate plane.
if triangle abc is rotated 180 degrees, reflected over the y - axis, and reflected over the x - axis to create triangle abc, where will point a lie?
(5, - 4)
(4, - 5)
(-4,5)
(-5,4)

Explanation:

Step1: Determine the original coordinates of point A

From the coordinate - plane, the coordinates of point \(A\) are \((- 5,4)\).

Step2: Apply the rotation of \(180^{\circ}\)

The rule for a \(180^{\circ}\) rotation about the origin \((x,y)\to(-x,-y)\). For point \(A(-5,4)\), after a \(180^{\circ}\) rotation, the coordinates become \((5, - 4)\).

Step3: Apply the reflection over the \(y\) - axis

The rule for a reflection over the \(y\) - axis is \((x,y)\to(-x,y)\). For the point \((5,-4)\) after reflection over the \(y\) - axis, the coordinates become \((-5,-4)\).

Step4: Apply the reflection over the \(x\) - axis

The rule for a reflection over the \(x\) - axis is \((x,y)\to(x,-y)\). For the point \((-5,-4)\) after reflection over the \(x\) - axis, the coordinates become \((-5,4)\).

Answer:

\((-5,4)\)