Common Core: High School - Geometry : Prove Simple Geometric Theorems by using Coordinates: CCSS.Math.Content.HSG-GPE.B.4

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

True or False:

The point  lies on a circle with a center of  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.

Now let's substitute for , , and .

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

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

 

 

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

True or False:

The point  lies on the ellipse

 

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.

 

 

 

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

 

 

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

True or False:

The point  lies on the ellipse 

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.

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

 

 

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

True or False:

The point  lies on a circle with a center of  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.

Now let's substitute for , , and .

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

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

 

 

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

True or False:

The point  lies on the line 

 

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.

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

 

 

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

True or False:

The point  lies on the line 

 

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.

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

 

 

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

True or False:

The point  lies on the ellipse

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.

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

 

 

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

True or False:

The point  lies on a circle with a center of  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.

Now let's substitute for , , and .

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

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

 

 

Example Question #9 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point  lies on the ellipse

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.

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

 

 

Example Question #10 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

The point  lies on the line 

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.

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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All Common Core: High School - Geometry Resources

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