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: Reflection rule about x - axis

When a point \((x,y)\) is reflected about the \(x -\)axis, the transformation rule is \((x,y)\to(x, - y)\).

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

For point \(A(2,0)\), 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 point \(B(-1,5)\), using the rule \((x,y)\to(x, - y)\), we get \(B'(-1,- 5)\).

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

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

Answer:

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