Question

give the coordinates of the point obtained from each reflection.
(a) reflect the point (5, 4) across the x - axis.
(□,□)
(b) reflect the point (5, 4) across the y - axis.
(□,□)

Explanation:

Part (a) Step1: Recall x - axis reflection rule

When a point \((x,y)\) is reflected across the \(x\) - axis, the \(x\) - coordinate remains the same, and the \(y\) - coordinate changes its sign. The rule is \((x,y)\to(x, - y)\).

Part (a) Step2: Apply the rule to \((5,4)\)

For the point \((5,4)\), \(x = 5\) and \(y = 4\). After reflection across the \(x\) - axis, the new \(x\) - coordinate is \(5\) (same as original) and the new \(y\) - coordinate is \(- 4\) (since we change the sign of \(y\)). So the reflected point is \((5,-4)\).

Part (b) Step1: Recall y - axis reflection rule

When a point \((x,y)\) is reflected across the \(y\) - axis, the \(y\) - coordinate remains the same, and the \(x\) - coordinate changes its sign. The rule is \((x,y)\to(-x,y)\).

Part (b) Step2: Apply the rule to \((5,4)\)

For the point \((5,4)\), \(x = 5\) and \(y = 4\). After reflection across the \(y\) - axis, the new \(x\) - coordinate is \(-5\) (change the sign of \(x\)) and the new \(y\) - coordinate is \(4\) (same as original). So the reflected point is \((-5,4)\).

Answer:

(a) \((5,-4)\)
(b) \((-5,4)\)