Lesson 15

Consider the parallelogram with vertices at \((0,0), (4,0), (2,3),\) and \((6,3)\). Where do the diagonals of this parallelogram intersect?

\((3,1.5)\)

\((4,2)\)

\((2,4)\)

\((3.5,3)\)

What is the midpoint of the line segment with endpoints \((1,\text-2)\) and \((9,8)\)?

\((3,5)\)

\((4,3)\)

\((5,3)\)

\((5,5)\)

Graph the image of triangle \(ABC\) under a dilation with center \(A\) and scale factor \(\frac{2}{3}\).

A quadrilateral has vertices \(A=(0,0), B=(2,4), C=(0,5),\) and \(D=(\text-2,1)\). Prove that \(ABCD\) is a rectangle.

A quadrilateral has vertices \(A=(0,0), B=(1,3), C= (0,4),\) and \(D=(\text-1,1)\). Select the most precise classification for quadrilateral \(ABCD\).

quadrilateral

parallelogram

rectangle

square

Write an equation whose graph is a line perpendicular to the graph of \(x=\text-7\) and which passes through the point \((\text-7,1)\).

Graph the equations \((x+1)^2+(y-1)^2=64\) and \(y = 1\). Where do they intersect?

A parabola has a focus of \((2, 5)\) and a directrix of \(y=1\). Decide whether each point on the list is on this parabola. Explain your reasoning.

1. \((\text{-}1,5)\)
2. \((2 ,3)\)
3. \((6,6)\)