Question

1. (3 points) when g(3, -5) is reflected in the line y = -2, what is the location of g?

g (____ , ____ )

1. (2 points) what are the coordinates of △def after it is reflected in the line y = -x?

a. d(5, 8), e(9, 6), f(3, 1)
b. d(-5, -8), e(-9, -6), f(-3, -1)
c. d(8, -5), e(6, -9), f(1, -3)

1. (1 point) bees jerod has installed beehives at points a, b, and c along a path. he wants to install a beehive at point d that is a reflection of point a across the path. where should jerod install the new hive?

d(____ , ____ )

Explanation:

Problem 1

Step1: Calculate the vertical distance

The \(y\) - coordinate of \(G(3,-5)\) and the line \(y = - 2\). The vertical distance \(d=\vert-2-(-5)\vert=\vert-2 + 5\vert=3\)

Step2: Find the \(y\) - coordinate of \(G'\)

Since we are reflecting over the line \(y=-2\), the \(x\) - coordinate remains the same (\(x = 3\)). The \(y\) - coordinate of \(G'\) is \(-2+3=1\)

Step1: Use the reflection rule over \(y=-x\)

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

For point \(D(-8,-5)\):
\(x=-8,y = - 5\), after reflection \((x',y')=(5,8)\)

For point \(E(-6,-9)\):
\(x=-6,y=-9\), after reflection \((x',y')=(9,6)\)

For point \(F(-1,-3)\):
\(x=-1,y=-3\), after reflection \((x',y')=(3,1)\)

Step1: Analyze the reflection over a vertical line (the path)

The path is a vertical line (assuming it is the \(y\) - axis - like vertical line in the grid). The \(x\) - coordinate of \(A(2,6)\) remains the same (\(x = 2\)) when reflected over a vertical line.

The vertical distance between \(A(2,6)\) and \(B(2,2)\) is \(d=\vert6 - 2\vert = 4\). The reflection of \(A\) over the "path" (assuming the path is at \(y = 2\)):
The \(y\) - coordinate of the reflection \(y=2-(6 - 2)=-2\)

Answer:

\(G'(3,1)\)

Problem 2