Lesson 7

Distances and Parabolas

Problem 1

The point $$(6,y)$$ is the same distance from $$(4,1)$$ as it is from the $$x$$-axis. What is the value of $$y$$?

Problem 2

A parabola is defined as the set of points the same distance from $$(6,2)$$ and the line $$y=4$$. Select all points that are on this parabola.

A:

$$(1,\text-2)$$

B:

$$(2,\text-1)$$

C:

$$(6,2)$$

D:

$$(7,3)$$

E:

$$(8,2)$$

Problem 3

Compare and contrast the parabolas with these definitions.

• parabola A: points that are the same distance from $$(0,4)$$ and the $$x$$-axis
• parabola B: points that are the same distance from $$(0,\text-6)$$ and the $$x$$-axis

Problem 4

Find the center and radius of the circle represented by the equation $$x^2+y^2-8y+5=0$$.

Solution

(From Unit 6, Lesson 6.)

Problem 5

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

Solution

(From Unit 6, Lesson 6.)

Problem 6

Write each expression as the square of a binomial.

1. $$x^2-12x+36$$
2. $$y^2+8y+16$$
3. $$w^2-16w+64$$

Solution

(From Unit 6, Lesson 5.)

Problem 7

Write an equation of a circle that is centered at $$(1,\text-4)$$ with a radius of 10.

Solution

(From Unit 6, Lesson 4.)

Problem 8

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.

Solution

(From Unit 5, Lesson 17.)

Problem 9

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

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