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9-12 Geometry Unit 6 Lesson 10

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 •Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

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Unit 6, Lesson 10

Parallel Lines in the Plane

Geometry

Practice

Problem 1

Select all equations that are parallel to the line \(2x + 5y = 8\).

\(y=\frac{2}{5}x + 4\)
\(y=\text-\frac{2}{5}x + 4\)
\(y-2=\frac{5}{2}(x+1)\)
\(y-2=\text-\frac{2}{5}(x+1)\)
\(10x+5y=40\)

Problem 2

Prove that \(ABCD\) is not a parallelogram.

<p>Quadrilateral ABCD. A at 1 comma 1, B at 4 comma 6, C at 9 comma 6, D at 5 comma 1.</p>

Problem 3

Write an equation of a line that passes through \((\text-1,2)\) and is parallel to a line with \(x\)-intercept \((3,0)\) and \(y\)-intercept \((0,1)\).

Problem 4

ForLesson 9: Equations of Lines

Write an equation of the line with slope \(\frac23\) that goes through the point \((\text-2, 5)\).

Problem 5

ForLesson 9: Equations of Lines

Priya and Han each wrote an equation of a line with slope \(\frac13\) that passes through the point \((1,2)\). Priya’s equation is \(y-2 = \frac13 (x-1)\) and Han’s equation is \(3y - x = 5\). Do you agree with either of them? Explain or show your reasoning.

Problem 6

ForLesson 8: Equations and Graphs

Match each equation with another equation whose graph is the same parabola.

\((x-3)^2+(y-2)^2=y^2\)
\((x-2)^2+(y-3)^2=(y+3)^2\)
\((x-3)^2+(y-4)^2=(y+2)^2\)
\((x-2)^2+(y-2)^2=(y+2)^2\)

\(y=\frac18(x-2)^2\)
\(y=\frac{1}{12}(x-2)^2\)
\(y=\frac{1}{4}(x-3)^2+1\)
\(y=\frac{1}{12}(x-3)^2+1\)

Problem 7

ForLesson 7: Distances and Parabolas

A parabola is defined as the set of points the same distance from \((\text-1, 3)\) and the line \(y=5\). Select the point that is on this parabola.

\((\text-1, 3)\)
\((0, 5)\)
\((3,0)\)
\((0,0)\)

Problem 8

ForLesson 2: Transformations as Functions

Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither.

\((x,y) \rightarrow (2x,y+2)\)
\((x,y) \rightarrow (2x,2y)\)
\((x,y) \rightarrow (x+2,y+2)\)