Question

△ efg has coordinates e(-2, -4), f(-8, 0), and g(-5, 3). what are the coordinates of the vertices of the image after a reflection in the y-axis?

a) ( e(2, -4) ), ( f(8, 0) ), and ( g(5, 3) )

b) ( e(-2, 4) ), ( f(-8, 0) ), and ( g(-5, -3) )

c) ( e(4, 2) ), ( f(0, 8) ), and ( g(-3, 5) )

d) ( e(4, -2) ), ( f(0, 8) ), and ( g(3, -5) )

Explanation:

Step1: Recall reflection over y - axis rule

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

Step2: Apply the rule to point E

For point \(E(-2,-4)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x = - 2\) and \(y=-4\). Then \(-x=-(-2) = 2\) and \(y=-4\). So the image of \(E\) is \(E'(2,-4)\).

Step3: Apply the rule to point F

For point \(F(-8,0)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x=-8\) and \(y = 0\). Then \(-x=-(-8)=8\) and \(y = 0\). So the image of \(F\) is \(F'(8,0)\).

Step4: Apply the rule to point G

For point \(G(-5,3)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x=-5\) and \(y = 3\). Then \(-x=-(-5)=5\) and \(y = 3\). So the image of \(G\) is \(G'(5,3)\).

Answer:

A) \(E'(2, - 4)\), \(F'(8, 0)\), and \(G'(5, 3)\)