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

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

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All Common Core: High School - Geometry Resources

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Example Questions

Example Question #11 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

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:

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.

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

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

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

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

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

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Example Question #12 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

True or False:

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

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

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.

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All Common Core: High School - Geometry Resources

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

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

All Common Core: High School - Geometry Resources

Example Questions

Example Question #11 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

Example Question #12 : Prove Simple Geometric Theorems By Using Coordinates: Ccss.Math.Content.Hsg Gpe.B.4

All Common Core: High School - Geometry Resources

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