Question

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

Explanation:

Part (a)

Step 1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is \((x,-y)\).

Step 2: Apply the rule to the point \((4,5)\)

For the point \((4,5)\), where \(x = 4\) and \(y=5\), after reflecting across the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So the new point is \((4,- 5)\).

Part (b)

Step 1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is \((-x,y)\).

Step 2: Apply the rule to the point \((4,5)\)

For the point \((4,5)\), where \(x = 4\) and \(y = 5\), after reflecting across the \(y\) - axis, the \(y\) - coordinate remains the same and the \(x\) - coordinate changes its sign. So the new point is \((-4,5)\).

Answer:

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

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