Question

question: 9
parallelogram is shown on the coordinate plane
parallelogram abcd (not shown) is the image of
parallelogram abcd after a rotation of 180° about the
origin.
which statements about parallelogram abcd are true?
select each correct statement.
a. (overline{ab}) is parallel to (overline{bc})
b. (overline{ab}) is parallel to (overline{ad})
c. (overline{ab}) is parallel to (overline{cd})
d. (overline{ad}) is parallel to (overline{bc})
e. (overline{ad}) is parallel to (overline{dc})
question: 10
point a is located at coordinates (-4, 3)
perform a reflection of point a over the y - axis, then a
perform a translation two units to the right. label this
new point a. what are the coordinates of point a?
point a =

Explanation:

Step1: Determine the coordinates of parallelogram ABCD

Assume \(A(-7,6)\), \(B(-4,6)\), \(C(-3,4)\), \(D(-6,4)\) (by observing the grid).

Step2: Apply the rotation rule \((x,y)\to(-x,-y)\)

For \(A(-7,6)\), \(A'=(7,-6)\); for \(B(-4,6)\), \(B'=(4,-6)\); for \(C(-3,4)\), \(C'=(3,-4)\); for \(D(-6,4)\), \(D'=(6,-4)\).

Step3: Check the parallel - side property of parallelogram

In a parallelogram, \(AB\parallel CD\) and \(AD\parallel BC\). After a \(180^{\circ}\) rotation about the origin, the parallel - side property is preserved. So \(\overline{A'B'}\parallel\overline{C'D'}\) and \(\overline{A'D'}\parallel\overline{B'C'}\).

For Question 10:

Step1: Apply the reflection rule over the \(y\) - axis

The reflection rule over the \(y\) - axis is \((x,y)\to(-x,y)\). For point \(A(-4,3)\), after reflection over the \(y\) - axis, the point is \((4,3)\).

Step2: Apply the translation rule

The translation rule for moving 2 units to the right is \((x,y)\to(x + 2,y)\). For the point \((4,3)\) after translation, \(x=4 + 2=6\), \(y = 3\).

Answer:

For Question 9: C, D.
For Question 10: \((6,3)\)