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High School Math : Coordinate Geometry

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Example Questions

Example Question #91 : Coordinate Geometry

A straight line passes through the points (1,3) and (2,2) .

What is the -intercept of this line?

Possible Answers:

(3,1)

(0,5)

(4,0)

(5,0)

(0,4)

Correct answer:

(4,0)

Explanation:

First calculate the slope:

$(\text{change in Y})/(\text{change in x}) = (1-2)/(3-2) = -1$

The standard equation for a line is Y=a*X + b .

In this equation, is the slope of the line, and is the -intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).

Plugging in (1,3) we get 3=-1*1 + b .

Therefore, b = 3 - (-1) =4 .

Our equation for the line is now:

Y= (-1)X + 4

To find the -intercept, we plug in y=0 :

0=(-1)x+4

x=4

Thus, the -intercept the point (4,0).

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Example Question #92 : Coordinate Geometry

Calculate the y-intercept of the line depicted by the equation below.

3x+6y=15

Possible Answers:

(0,5)

(2.5,0)

(0,2.5)

(0,6)

(5,0)

Correct answer:

(0,2.5)

Explanation:

To find the y-intercept, let equal 0.

3(0)+6y=15

We can then solve for the value of .

6y=15

$y=\frac{15}{6}=2.5$

The y-intercept will be (0,2.5) .

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Example Question #93 : Coordinate Geometry

What is the x-intercept of 2y=3x+5 ?

Possible Answers:

$-\frac{3}{5}$

$\frac{6}{5}$

$\frac{3}{5}$

$-\frac{10}{3}$

$-\frac{5}{3}$

Correct answer:

$-\frac{5}{3}$

Explanation:

To find the x-intercept, set y equal to zero and solve:

2y=3x+5

2(0)=3x+5

0=3x+5

Subtract from both sides:

-5=3x

Divide both sides by to isolate x:

$\frac{-5}{3}=x$

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Example Question #94 : Coordinate Geometry

What is the y-intercept of the equation?

$y=\frac{2}{3}x+ 12$

Possible Answers:

(0,0)

(0,12)

(0,4)

(0,3)

(0,8)

Correct answer:

(0,12)

Explanation:

$y=\frac{2}{3}x+ 12$

To find the y-intercept, we set the value equal to zero and solve for the $\small y$ value.

$y= \frac{2}{3} (0) +12$

y=12

Since the y-intercept is a point, we will need to convert our answer to point notation.

(0,12)

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Example Question #1 : How To Find The Equation Of A Curve

What line goes through points (-3,-7) and (2,3) ?

Possible Answers:

y=2x-1

y=2x+5

$y=\frac{-1}{2}x+3$

y=-2x-4

$y=\frac{1}{2}x-3$

Correct answer:

y=2x-1

Explanation:

First, we find the slope between the two points:

$P_{1}=(-3,-7)$ and $P_{2}=(2,3)$

$m= \frac{y_{2} - y_{1}}{x_{2}-x_{1}}=\frac{3-(-7)}{2-(-3)}=\frac{10}{5}=2$

Plug the slope and one point into the slope-intercept form to calculate the intercept:

y=mx+b

3=2(2)+b

b=-1

Thus the equation between the points becomes y=2x-1 .

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Example Question #1 : How To Find The Equation Of A Circle

The center of a circle is (2, 4) and its radius is . Which of the following could be the equation of the circle?

Possible Answers:

$(x - 2)^{2} + (y - 4)^{2} = 10$

$(x - 2)^{2} + (y - 4)^{2} = 100$

$x^{2} + y^{2} = 100$

$2x^{2} + 4y^{2} = 100$

$(x + 2)^{2} + (y + 4)^{2} = 100$

Correct answer:

$(x - 2)^{2} + (y - 4)^{2} = 100$

Explanation:

The general equation of a circle is $(x - h)^{2} + (y - k)^{2} = r^{2}$ , where the center of the circle is (h, k) and the radius is .

Thus, we plug the values given into the above equation to get $(x - 2)^{2} + (y - 4)^{2} = 100$ .

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Example Question #2 : How To Find The Equation Of A Circle

Which one of these equations accurately describes a circle with a center of (2,3) and a radius of ?

Possible Answers:

x^2+y^2=25

$\sqrt{x^2+y^2-3^2-2^2}=5$

(x^2+4)-(y^2+9)=25

(x-2)^2+(y-3)^2-25=0

(x-3)^2+(y-2)^2=25

Correct answer:

(x-2)^2+(y-3)^2-25=0

Explanation:

The standard formula for a circle is (x-a)^2+(y-b)^2=r^2 , with (a,b) the center of the circle and the radius.

Plug in our given information.

(x-a)^2+(y-b^2)=r^2

(x-2)^2+(y-3)^2=25

This describes what we are looking for. This equation is not one of the answer choices, however, so subtract from both sides.

(x-2)^2+(y-3)^2-25=0

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High School Math : Coordinate Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #91 : Coordinate Geometry

Example Question #92 : Coordinate Geometry

Example Question #93 : Coordinate Geometry

Example Question #94 : Coordinate Geometry

Example Question #1 : How To Find The Equation Of A Curve

Example Question #1 : How To Find The Equation Of A Circle

Example Question #2 : How To Find The Equation Of A Circle

All High School Math Resources

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