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 x - axis.
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 the reflection rule

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

Step2: Apply the rule to point \(A(2,0)\)

For \(A(2,0)\), using the rule \((x,y)\to(x, - y)\), we get \(A'(2,0)\) (since \(-0 = 0\)).

Step3: Apply the rule to point \(B(-1,5)\)

For \(B(-1,5)\), using the rule \((x,y)\to(x, - y)\), we get \(B'(-1,-5)\).

Step4: Apply the rule to point \(C(4,3)\)

For \(C(4,3)\), using the rule \((x,y)\to(x, - y)\), we get \(C'(4,-3)\).

Answer:

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