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HSPT Math : How to do coordinate geometry

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Example Questions

Example Question #1 : How To Do Coordinate Geometry

A deer walks in a straight line for 8 hours. At the end of its journey, the deer is 30 miles north and 40 miles east of where it began. What was the average speed of the deer?

Possible Answers:

12.5 miles per hour

miles per hour

6.25 miles per hour

miles per hour

Correct answer:

6.25 miles per hour

Explanation:

To find the speed of the deer, you must have the distance traveled and the time.

The distance is found using the Pythagorean Theorem:

A^2 + B^2 = C^2

$C = {\sqrt{A^2+ B^2}}$

$C = \sqrt{30^2 + 40^2}$

$C = \sqrt{2500} = 50$

The answer must be in miles per hour so the total miles are divided by the hours to get the final answer:

$\frac{miles}{hour} = \frac{50}{8} = 6.25 mph$

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Example Question #1 : How To Do Coordinate Geometry

You are looking at a map of your town and your house is located at the coordinate (0,0). Your school is located at the point (3,4). If each coordinate distance is 1.3 miles, how far away is your school?

Possible Answers:

$9.1\ miles$

$32.5\ miles$

$7\ miles$

$5\ miles$

$6.5\ miles$

Correct answer:

$6.5\ miles$

Explanation:

The coordinate length between you and your school is equivalent to the hypotenuse of a right triangle with sides of 3 and 4 units:

x^2=3^2+4^2

x^2=9+16

x^2=25

x=5

The distance is 5 coordinate lengths, and each coordinate length corresponds to 1.3 miles of distance, so

$5\times 1.3 =6.5\hspace{1 mm}miles$

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Example Question #1 : Coordinate Geometry

Which of the following is a vertex of the square?

Question_12

Possible Answers:

$\small (-1,2)$

$\small (1,-4)$

$\small (-2,1)$

$\small (2,4)$

$\small (-1,-4)$

Correct answer:

$\small (-1,2)$

Explanation:

The coordinates of a point are determined by the distance from the origin. The first point in the ordered pair is the number of units to the left or right of the origin. Negative numbers indicate the number of units to the left while positive numbers indicate the number of units to the right. The second number indicates the number of units above or below the origin. Positive numbers indicate the number of units above while negative numbrs indicate the number of units below the origin. The vertices of the square are:
$\small (-1,2); (-1,4); (1,2); (-1,4)$

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Example Question #1 : How To Find The Points On A Coordinate Plane

Which of the following points will you find on the -axis?

Possible Answers:

(30,30)

(0,-30)

(30, 0)

(30,-30)

(-30,30)

Correct answer:

(0,-30)

Explanation:

A point is located on the -axis if and only if it has -coordinate (first coordinate) 0. Of the five choices, only (0,-30) fits that description.

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Example Question #281 : Geometry

Which of the following points is on the -axis?

Possible Answers:

(0,10)

(20,1)

(10,10)

(20,0)

(0,20)

Correct answer:

(20,0)

Explanation:

A point is located on the -axis if and only if it has a -coordinate equal to zero. So the answer is (20,0) .

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Example Question #4 : How To Do Coordinate Geometry

The point (-1,-1) is reflected across x=1 . What is the new point?

Possible Answers:

(3,-1)

(0,-1)

(4,-1)

(0,1)

(2,-1)

Correct answer:

(3,-1)

Explanation:

The horizontal distance from point (-1,-1) to the vertical line x=1 is two units. Since this point is reflected across x=1 , the new point will also be 2 units to the right of line x=1 .

Therefore, the correct answer is: (3,-1)

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Example Question #1 : How To Do Coordinate Geometry

What is the slope given the following two points? $(2,3) \textup{ and } (3,-8)$

Possible Answers:

$-\frac{1}{11}$

$-\frac{1}{5}$

$\frac{1}{5}$

Correct answer:

Explanation:

Write the slope formula and substitute the two points.

$m=\frac{y_2-y_1}{x_2-x_1}= \frac{-8-3}{3-2}= \frac{-11}{1} = -11$

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Example Question #4 : How To Do Coordinate Geometry

The lines of which two of the following equations are perpendicular to each other?

(I) $y= \frac{6}{11} x$

(II) $y= - \frac{6}{11} x$

(III) $y= - \frac{11}{6} x$

Possible Answers:

I and II

I and III

II and III

No two of the equations given are represented by lines that are perpendicular to each other.

Correct answer:

I and III

Explanation:

All three equations are in slope-intercept form y = mx+ b , so the slope of each line is the coefficient of :

(I) $y= \frac{6}{11} x$ - the slope is $\frac{6}{11}$

(II) $y= - \frac{6}{11} x$ - the slope is $- \frac{6}{11}$

(III) $y= - \frac{11}{6} x$ - the slope is $- \frac{11}{6}$

Two lines are perpendicular if and only if the product of their slopes is .

The product of the slopes of the lines in I and II is

$\frac{6}{11} \times \left (- \frac{6}{11} \right )= - \frac{6 \times 6 }{11 \times 11} =- \frac{36 }{121} \ne -1$

The product of the slopes of the lines in II and III is

$- \frac{6}{11} \times \left (- \frac{11} {6}\right )= + \frac{6 \times 11 }{11 \times 6} = \frac{66}{66} = 1 \ne -1$

The product of the slopes of the lines in I and III is

$\frac{6}{11} \times \left (- \frac{11} {6}\right )= - \frac{6 \times 11 }{11 \times 6} =- \frac{66}{66} = -1$

This makes the lines in I and III perpendicular, and this is the correct choice.

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Example Question #5 : How To Do Coordinate Geometry

Begin at the origin of the rectangular coordinate plane. Move up three units, left seven units, and down nine units. Give the coordinates of your current location.

Possible Answers:

(-7, -6)

( 7, -6)

(-7,6)

( 7,6)

Correct answer:

(-7, -6)

Explanation:

Since you have moved left seven units, you have moved seven units in a negative horizontal direction, making the -coordinate of your current location .

Since you have moved up three units and down nine units, you have moved six units down - this is six units in a negative vertical direction, making the -coordinate of your current location .

Therefore, the ordered pair for your current location is (-7, -6) .

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Example Question #4 : How To Find A Line On A Coordinate Plane

Billy set up a ramp for his toy cars. He did this by taking a wooden plank and putting one end on top of a brick that was 3 inches high. He then put the other end on top of a box that was 9 inches high. The bricks were 18 inches apart. What is the slope of the plank?

Possible Answers:

$\frac{1}{18}$

$\frac{1}{3}$

$\frac{5}{9}$

$\frac{3}{18}$

Correct answer:

$\frac{1}{3}$

Explanation:

The value of the slope (m) is rise over run, and can be calculated with the formula below:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The coordinates of the first end of the plank would be (0,3), given that this is the starting point of the plank (so x would be 0), and y would be 3 since the brick is 3 inches tall.

The coordinates of the second end of the plank would be (18,9) since the plank is 18 inches long (so x would be 18) and y would be 9 since the box was 9 inches tall at the other end.

From this information we know that we can assign the following coordinates for the equation:

$\left(x_{1},y_{1}\right) = (0,3)$ and $(x_{2}, y_{2})= (18,9)$

Below is the solution we would get from plugging this information into the equation for slope:

$m = \frac{9-3}{18-0}}$

This reduces to $\frac{6}{18} =\frac{1}{3}$

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HSPT Math : How to do coordinate geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : How To Do Coordinate Geometry

Example Question #1 : How To Do Coordinate Geometry

Example Question #1 : Coordinate Geometry

Example Question #1 : How To Find The Points On A Coordinate Plane

Example Question #281 : Geometry

Example Question #4 : How To Do Coordinate Geometry

Example Question #1 : How To Do Coordinate Geometry

Example Question #4 : How To Do Coordinate Geometry

Example Question #5 : How To Do Coordinate Geometry

Example Question #4 : How To Find A Line On A Coordinate Plane

All HSPT Math Resources

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