Question

8.g.a.3
triangle efg has vertices e(-3, 1), f(1, 1), and g(4, 5). find the coordinates of the image of point f after a reflection across the x-axis.

○ (-1, -1)
○ (1, 1)
○ (1, -1)
○ (-1, 1)

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. Mathematically, if we have a point \(P(x,y)\), after reflection across the \(x\) - axis, the image \(P'\) has coordinates \((x, - y)\).

Step2: Identify coordinates of point F

We are given that the coordinates of point \(F\) are \((1,1)\). Here, \(x = 1\) and \(y=1\).

Step3: Apply the reflection rule

Using the rule for reflection across the \(x\) - axis \((x,y)\to(x, - y)\), for the point \(F(1,1)\), the \(x\) - coordinate \(x = 1\) remains unchanged, and the \(y\) - coordinate \(y = 1\) becomes \(-y=- 1\). So the coordinates of the image of point \(F\) after reflection across the \(x\) - axis are \((1,-1)\).

Answer:

\((1, - 1)\) (corresponding to the option with coordinates \((1, - 1)\))