Question

triangle abc has coordinates a(2, 0), b(-1, 5), and c(4, 3). determine the coordinates of the vertices of the image after a reflection in the...
a) a(-2, 0), b(-1, -5), and c(4, 3)
b) a(2, 0), b(-1, -5), and c(4, -3)
c) a(-2, 0), b(1, 5), and c(4, 3)
d) a(2, 0), b(1, 5), and c(-4, -3)

Explanation:

Step1: Recall Reflection Over x - axis

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

Step2: Reflect Point A

For point \(A(2,0)\), applying the reflection rule: \(x = 2\), \(y = 0\), so \(A'=(2,- 0)=(2,0)\) (since \(-0 = 0\)).

Step3: Reflect Point B

For point \(B(-1,5)\), applying the reflection rule: \(x=-1\), \(y = 5\), so \(B'=(-1,-5)\).

Step4: Reflect Point C

For point \(C(4,3)\), applying the reflection rule: \(x = 4\), \(y = 3\), so \(C'=(4,-3)\).

Answer:

B) \(A'(2,0)\), \(B'(-1,-5)\), and \(C'(4,-3)\)