Question

reflect the figure over the line ( y = -1 ).
plot all of the points of the reflected figure.
you may click a plotted point to delete it.

Explanation:

Step1: Recall the reflection formula

When reflecting a point \((x,y)\) over the line \(y = k\), the formula is \((x,2k - y)\). Here \(k=-1\), so the formula becomes \((x,2\times(-1)-y)=(x,-2 - y)\)

Step2: Identify the original points

Assume the original points of the triangle are \(A(-3,5)\), \(B(-1,5)\), \(C(-2,4)\)

Step3: Apply the reflection formula

For point \(A(-3,5)\):
Substitute \(x=-3\) and \(y = 5\) into \((x,-2 - y)\)
\(x=-3\), \(2k - y=-2-5=-7\), so the reflected point \(A'(-3,-7)\)

For point \(B(-1,5)\):
Substitute \(x = -1\) and \(y = 5\) into \((x,-2 - y)\)
\(x=-1\), \(2k - y=-2 - 5=-7\), so the reflected point \(B'(-1,-7)\)

For point \(C(-2,4)\):
Substitute \(x=-2\) and \(y = 4\) into \((x,-2 - y)\)
\(x=-2\), \(2k - y=-2-4=-6\), so the reflected point \(C'(-2,-6)\)

Answer:

Plot the points \((-3,-7)\), \((-1,-7)\) and \((-2,-6)\)