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ISEE Middle Level Quantitative : How to find the points on a coordinate plane

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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All ISEE Middle Level Quantitative Resources

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Example Questions

Example Question #1 : Geometry

Choose the best answer from the four choices given.

The point (15, 6) is on which of the following lines?

Possible Answers:

$y=\frac{-1}{2}x+7$

$y=\frac{1}{2}x-7$

$y=-\frac{2}{3}x+4$

$y=\frac{2}{3}x-4$

Correct answer:

$y=\frac{2}{3}x-4$

Explanation:

For this problem, simply plug in the values for the point (15,6) into the different equations (15 for the -value and 6 for the -value) to see which one fits.

$(6)=\frac{1}{2}(15)-7$ (NO)

$(6)=\frac{2}{3}(15)-4$ (YES!)

$(6)=\frac{-1}{2}(15)+7$ (NO)

$(6)=\frac{-2}{3}(15)+4$ (NO)

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

Choose the best answer from the four choices given.

What is the point of intersection for the following two lines?

$y=\frac{3}{4}x-11$

$y=\frac{-5}{6}x+8$

Possible Answers:

$\left ( 12,-2 \right )$

$\left ( 8,-5 \right )$

$\left ( 6,3 \right )$

$\left ( 0,-11 \right )$

Correct answer:

$\left ( 12,-2 \right )$

Explanation:

At the intersection point of the two lines the - and - values for each equation will be the same. Thus, we can set the two equations as equal to each other:

$\frac{3}{4}x-11=\frac{-5}{6}x+8$

$\frac{3}{4}x=\frac{-5}{6}x+19$

$\frac{9}{12}x=\frac{-10}{12}x+19$

$\frac{19}{12}x=19$

$(\frac{12}{19})(\frac{19}{12}x)=19 (\frac{12}{19})$

$\large x=12$

$y=\frac{3}{4}(12)-11= -2$

point of intersection $=\left ( 12,-2 \right )$

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Example Question #3 : How To Find The Points On A Coordinate Plane

Choose the best answer from the four choices given.

What is the -intercept of the line represented by the equation

$y=\frac{7}{9}x-3\ ?$

Possible Answers:

$3\frac{6}{7}$

$-3\frac{6}{7}$

Correct answer:

$3\frac{6}{7}$

Explanation:

In the formula y=mx+b , the y-intercept is represented by (because if you set to zero, you are left with y=b ).

Thus, to find the -intercept, set the value to zero and solve for .

$0=\frac{7}{9}x-3$

$\frac{-7}{9}x=-3$

$(\frac{-9}{7})\frac{-7}{9}x=-3 (\frac{-9}{7})$

$x=\frac{27}{7}=3\frac{6}{7}$

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Example Question #1 : Coordinate Geometry

The ordered pair (-1,4) is in which quadrant?

Possible Answers:

Quadrant I

Quadrant V

Quadrant II

Quadrant III

Quadrant IV

Correct answer:

Quadrant II

Explanation:

There are four quadrants in the coordinate plane. Quadrant I is the top right, and they are numbered counter-clockwise. Since the x-coordinate is , you go to the left one unit (starting from the origin). Since the y-coordinate is , you go upwards four units. Therefore, you are in Quadrant II.

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Example Question #1 : Coordinate Geometry

If angles s and r add up to 180 degrees, which of the following best describes them?

Possible Answers:

Complementary

Acute

Obtuse

Supplementary.

Correct answer:

Supplementary.

Explanation:

Two angles that are supplementary add up to 180 degrees. They cannot both be acute, nor can they both be obtuse. Therefore, "Supplementary" is the correct answer.

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Example Question #6 : How To Find The Points On A Coordinate Plane

The lines of the equations

y= 3x

and

x+y = 8

intersect at a point (X, Y) .

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

Correct answer:

(b) is the greater quantity

Explanation:

If y= 3x and x+y = 8 , we can substitute in the second equation as follows:

x+y = 8

x+ 3x = 8

1x+ 3x = 8

(1 + 3)x = 8

4x= 8

$4x \div 4 = 8 \div 4$

x = 2

Substitute:

y= 3x

$y= 3 \cdot 2$

y = 6

y > x

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : How to find the points on a coordinate plane

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #1 : Geometry

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

Example Question #3 : How To Find The Points On A Coordinate Plane

Example Question #1 : Coordinate Geometry

Example Question #1 : Coordinate Geometry

Example Question #6 : How To Find The Points On A Coordinate Plane

All ISEE Middle Level Quantitative Resources

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