Unit 6, Lesson 7

Distances and Parabolas

Geometry

Practice

Problem 1

Student Task Statement

The point is the same distance from as it is from the -axis. What is the value of ?

Practice

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Problem 2

Student Task Statement

A parabola is defined as the set of points the same distance from and the line . Select all points that are on this parabola.

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Problem 3

Student Task Statement

Compare and contrast the parabolas with these definitions.

parabola A: points that are the same distance from and the -axis
parabola B: points that are the same distance from and the -axis

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Problem 4

ForLesson 6: Completing the Square

Student Task Statement

Find the center and radius of the circle represented by the equation .

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Problem 5

ForLesson 6: Completing the Square

Student Task Statement

Match each expression with the value needed in the box in order for the expression to be a perfect square trinomial.

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Problem 6

ForLesson 5: Squares and Circles

Student Task Statement

Write each expression as the square of a binomial.

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Problem 7

ForLesson 4: Distances and Circles

Student Task Statement

Write an equation of a circle that is centered at with a radius of 10.

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Problem 8

ForLesson 17: Volume and Density

Student Task Statement

The density of water is 1 gram per cm³. An object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. Will a solid bar of soap shaped like a rectangular prism with mass 1.048 kilograms and dimensions 5.6 centimeters, 13 centimeters, and 16 centimeters float or sink? Explain your reasoning.

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Problem 9

ForLesson 5: Construction Techniques 3: Perpendicular Lines and Angle Bisectors

Student Task Statement

Jada has this idea for bisecting angle . First she draws a circle with center through . Then she constructs the perpendicular bisector of .

<p>Circle with center point B, central angle ABD, DA segment, point C is on BD outside of the circle.</p>

<p>Circle with center point B, central angle ABD, DA segment, diameter drawn through B and the midpoint of DA, point C is on BD outside of the circle.</p>

Does Jada's construction work? Explain your reasoning. You may assume that the perpendicular bisector of line segment is the set of points equidistant from and .

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Distances and Parabolas

Practice

Problem 1

Student Task Statement

Problem 2

Student Task Statement

Problem 3

Student Task Statement

Problem 4

Student Task Statement

Problem 5

Student Task Statement

Problem 6

Student Task Statement

Problem 7

Student Task Statement

Problem 8

Student Task Statement

Problem 9

Student Task Statement

Lesson 7 Resources