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9-12 Geometry Unit 6 Lesson 7

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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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Unit 6, Lesson 7

Distances and Parabolas

Geometry

Practice

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.

\((1,\text-2)\)
\((2,\text-1)\)
\((6,2)\)
\((7,3)\)
\((8,2)\)

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

ForLesson 6: Completing the Square

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

Problem 5

ForLesson 6: Completing the Square

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

\(x^2 + 14x + \boxed{\phantom{3}}\)
\(x^2 -\frac12 x + \boxed{\phantom{3}}\)
\(c^2 - 10c + \boxed{\phantom{3}}\)
\(z^2 +z + \boxed{\phantom{3}}\)

\(\frac{1}{16}\)
49
25
\(\frac14\)

Problem 6

ForLesson 5: Squares and Circles

Write each expression as the square of a binomial.

\(x^2-12x+36\)
\(y^2+8y+16\)
\(w^2-16w+64\)

Problem 7

ForLesson 4: Distances and Circles

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

Problem 8

ForLesson 17: Volume and Density

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.

Problem 9

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

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 \(AD\).

<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 \(AD\) is the set of points equidistant from \(A\) and \(D\).