How to find the points on a coordinate plane

ISEE Middle Level Quantitative Reasoning · Learn by Concept

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

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Choose the best answer from the four choices given.

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

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

$3\frac{6}{7}$

CORRECT

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

Explanation

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

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

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

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

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

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

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

Supplementary.

CORRECT

Complementary

Acute

Obtuse

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.

The lines of the equations

and

intersect at a point .

Which is the greater quantity?

(a)

(b)

(b) is the greater quantity

CORRECT

(a) is the greater quantity

(a) and (b) are equal

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

Explanation

If and , we can substitute in the second equation as follows:

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

Substitute:

$y= 3 \cdot 2$

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( - 300, 200 \right )$ and $\left ( -200, 300 \right )$ . Give the coordinates of the midpoint of the segment.

CORRECT

Explanation

The -coordinate of the midpoint can be found by dividing the sum of the -coordinates of the endpoints by 2:

$[ -300 + (-200) ] \div 2 = [ -(300 + 200) ] \div 2 = -500 \div 2 = - (500 \div 2) = -250$

The -coordinate of the midpoint is found similarly:

$(200 + 300) \div 2 = 500 \div 2 = 250$ .

The correct response is .

The ordered pair is in which quadrant?

Quadrant II

CORRECT

Quadrant I

Quadrant III

Quadrant IV

Quadrant V

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.

Angela plotted points A through E on the coordinate plane shown below.

Points_grid

Which point is located at the ordered pair

Point B

CORRECT

Point A

Point C

Point D

Point E

Explanation

Start at point (0, 0) in the bottom, left corner of the the coordinate plane. From there, count right 2 spaces. This is the first number in the given ordered pair. From that point, count up 8 spaces. This is the second number in the given ordered pair.

By moving right 2 and up 8, you should have found Point B.

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

CORRECT

Explanation

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

Choose the best answer from the four choices given.

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

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

CORRECT

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

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

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

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)

Choose the best answer from the four choices given.

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

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

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

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

CORRECT

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

$\left ( 6,3 \right )$

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

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: