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Common Core: High School - Geometry : Expressing Geometric Properties with Equations

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point (7, 6) lies on a circle with a center of (-9, 10) and a radius .

Possible Answers:

True

False

Correct answer:

False

Explanation:

In order to solve this problem, we need to write out the general equation of a circle.

$\left(- h + x\right)^{2} + \left(- k + y\right)^{2} = r^{2}$

Now let's substitute for , , and .

$\left(x + 9\right)^{2} + \left(y - 10\right)^{2} = 9$

Now we can plug in the point, and see if it lies on the circle.

272 = 9

The point does not lie on the circle, because each side is not equal to each other. So our answer is False.

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Example Question #2 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point (10, 8) lies on the line

y = 4 x + 7

Possible Answers:

False

True

Correct answer:

False

Explanation:

In order to solve this problem, we need to plug in the point and see if both sides of the equation are equal or not.

y = 4 x + 7

$\\8 = 4 (10) + 7 \\8=40+7$

8 = 47

The point does not lie in the line, because each side is not equal to each other. So our answer is False.

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Example Question #3 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point (4, 24) lies on the line

y = 9 x + 5

Possible Answers:

True

False

Correct answer:

False

Explanation:

In order to solve this problem, we need to plug in the point and see if both sides of the equation are equal or not.

y = 9 x + 5

$\\24 = 9 (4) + 5 \\24=36+5$

24 = 41

The point does not lie in the line, because each side is not equal to each other. So our answer is False.

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Example Question #4 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point (9, 10) lies on the ellipse

$\frac{1}{6} \left(x - 1\right)^{2} + \frac{1}{10} \left(y + 1\right)^{2} = 1$

Possible Answers:

True

False

Correct answer:

False

Explanation:

In order to solve this problem, we need to plug in the point, and see if both sides of the equation are equal.

$\frac{1}{6} \left(x - 1\right)^{2} + \frac{1}{10} \left(y + 1\right)^{2} = 1$

$\frac{1}{6} \left(9 - 1\right)^{2} + \frac{1}{10} \left(10 + 1\right)^{2} = 1$

$\frac{1}{6} \left(8\right)^{2} + \frac{1}{10} \left(11\right)^{2} = 1$

$\frac{1}{6} (64) + \frac{1}{10} (121) = 1$

$\frac{683}{30} = 1$

The point does not lie on the ellipse, because each side is not equal to each other. So our answer is False.

Report an Error

Example Question #5 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point (5, 5) lies on a circle with a center of (9, 19) and a radius .

Possible Answers:

True

False

Correct answer:

False

Explanation:

In order to solve this problem, we need to write out the general equation of a circle.

$\left(- h + x\right)^{2} + \left(- k + y\right)^{2} = r^{2}$

Now let's substitute for , , and .

$\left(x - 9\right)^{2} + \left(y - 19\right)^{2} = 1$

Now we can plug in the point, and see if it lies on the circle.

212 = 1

The point does not lie on the circle, because each side is not equal to each other. So our answer is False.

Report an Error

Example Question #6 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point (1, 7) lies on the ellipse

$\frac{1}{6} \left(x - 1\right)^{2} + \frac{1}{14} \left(y + 3\right)^{2} = 1$

Possible Answers:

False

True

Correct answer:

False

Explanation:

In order to solve this problem, we need to plug in the point, and see if both sides of the equation are equal.

$\frac{1}{6} \left(x - 1\right)^{2} + \frac{1}{14} \left(y + 3\right)^{2} = 1$

$\frac{1}{6} \left(1 - 1\right)^{2} + \frac{1}{14} \left(7 + 3\right)^{2} = 1$

$\frac{1}{14} \left(100\right) = 1$

$\frac{50}{7} = 1$

The point does not lie on the ellipse, because each side is not equal to each other. So our answer is False.

Report an Error

Example Question #7 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point (7, 34) lies on the line

y = 3 x + 8

Possible Answers:

False

True

Correct answer:

False

Explanation:

In order to solve this problem, we need to plug in the point and see if both sides of the equation are equal or not.

y = 3 x + 8

$\\34 = 3 (7) + 8 \\34=21+8$

34 = 29

The point does not lie in the line, because each side is not equal to each other. So our answer is False.

Report an Error

Example Question #8 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point (5, 10) lies on the line

y = 2 x + 5

Possible Answers:

False

True

Correct answer:

False

Explanation:

In order to solve this problem, we need to plug in the point and see if both sides of the equation are equal or not.

y = 2 x + 5

10 = 2 (5) + 5

10 = 15

The point does not lie in the line, because each side is not equal to each other. So our answer is False.

Report an Error

Example Question #41 : Expressing Geometric Properties With Equations

True or False:

The point (7, 4) lies on the ellipse

$\frac{1}{5} \left(x - 6\right)^{2} + \frac{1}{6} \left(y - 6\right)^{2} = 1$

Possible Answers:

True

False

Correct answer:

False

Explanation:

In order to solve this problem, we need to plug in the point, and see if both sides of the equation are equal.

$\frac{1}{5} \left(x - 6\right)^{2} + \frac{1}{6} \left(y - 6\right)^{2} = 1$

$\frac{1}{5} \left(7 - 6\right)^{2} + \frac{1}{6} \left(4 - 6\right)^{2} = 1$

$\frac{1}{5} \left(1\right)^{2} + \frac{1}{6} \left(-2\right)^{2} = 1$

$\frac{13}{15} = 1$

The point does not lie on the ellipse, because each side is not equal to each other. So our answer is False.

Report an Error

Example Question #42 : Expressing Geometric Properties With Equations

True or False:

The point (-6, 6) lies on a circle with a center of (8, -15) and a radius .

Possible Answers:

False

True

Correct answer:

False

Explanation:

In order to solve this problem, we need to write out the general equation of a circle.

$\left(- h + x\right)^{2} + \left(- k + y\right)^{2} = r^{2}$

Now let's substitute for , , and .

$\left(x - 8\right)^{2} + \left(y + 15\right)^{2} = 4$

Now we can plug in the point, and see if it lies on the circle.

637 = 4

The point does not lie on the circle, because each side is not equal to each other. So our answer is False.

Report an Error

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

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Common Core: High School - Geometry : Expressing Geometric Properties with Equations

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #1 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #2 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #3 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #4 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #5 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #6 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #7 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #8 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #41 : Expressing Geometric Properties With Equations

Example Question #42 : Expressing Geometric Properties With Equations

All Common Core: High School - Geometry Resources

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