How to find the points on a coordinate plane

Help Questions

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

Questions 1 - 9

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( 4 \frac{1}{3}, - 4 \frac{1}{3}\right )$ and $\left ( 12, 12\right )$ . Give the coordinates of the midpoint of the segment.

$\left ( 8 \frac{1}{6}, 3 \frac{5}{6} \right )$

$\left ( 16 \frac{1}{3}, 7 \frac{2}{3} \right )$

$\left ( 7 \frac{2}{3}, 16 \frac{1}{3}\right )$

$\left ( 3 \frac{5}{6} , 8 \frac{1}{6} \right )$

Explanation

The -coordinate of the midpoint is half the sum of the -coordinates of the endpoints:

$\frac{1}{2} \left ( 4 \frac{1}{3} + 12 \right )$

$= \frac{1}{2} \times 16 \frac{1}{3}$

$= \frac{1}{2} \times \frac{49}{3}$

$= \frac{49}{6}$

$=8 \frac{1}{6}$

The -coordinate of the midpoint is found similarly:

$\frac{1}{2} \left (- 4 \frac{1}{3} + 12 \right )$

$= \frac{1}{2} \left (12 - 4 \frac{1}{3} \right )$

$= \frac{1}{2} \times 7 \frac{2}{3}$

$= \frac{1}{2} \times \frac{23}{3}$

$= \frac{23}{6}$

$= 3 \frac{5}{6}$

The midpoint has coordinates $\left ( 8 \frac{1}{6}, 3 \frac{5}{6} \right )$ .

In which quadrant or on which axis will you find the point ?

The -axis

Quadrant I

Quadrant II

Quadrant III

Explanation

The point does not move in any direction on the -axis, but does move units up on the -axis. Therefore, the point is located only on the -axis.

Which of the following points is in Quadrant II on the coordinate plane?

Explanation

All points in Quadrant II have negative -coordinates and positive -coordinates. The only answer that fulfills these criteria is .

In which quadrant or on which axis will you find the point ?

Quadrant III

Quadrant I

Quadrant II

Quadrant IV

The -axis

Explanation

By definition, a point with a negative -coordinate and a negative -coordinate lies in Quadrant III on the coordinate plane.

In which quadrant or on what axis will you find the point ?

Quadrant II

Quadrant I

Quadrant III

Quadrant IV

The -axis

Explanation

The point has a negative coordinate and a positive coordinate. By definition, any point on a coordinate plane with these characteristics is located in Quadrant II.

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( - 10, -20 \right )$ and $\left ( -20,10 \right )$ . Give the coordinates of the midpoint of the segment.

Explanation

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

$\left [(-10 ) + (-20) \right ] \div 2 = \left [-(10 + 20) \right ] \div 2 = -30 \div 2 = -15$

The -coordinate of the midpoint is found similarly:

$\left [ (-20)+ 10 \right ] \div 2 = \left [-(20-10) \right ] \div 2 = -10 \div 2 = -5$

The coordinates of the midpoint are .

In which quadrant or on which axis will we find the point ?

The -axis

Quadrant I

Quadrant IV

Quadrant II

Explanation

By definition, any point in the coordinate plane that has a non-zero value -coordinate and a zero-value -coordinate is on the -axis.

In which quadrant or on which axis of the coordinate plane will you find the point ?

Quadrant IV

Quadrant I

Quadrant II

Quadrant III

The -axis

Explanation

A point with a positive -coordinate and a negative -coordinate can be found in Quadrant IV.

Which of the following points would be located in Quadrant III?

Explanation

By definition, a point on the coordinate plane that is in Quadrant III must have both a negative coordinate and a negative coordinate. The only answer choice that satisfies both of these conditions is .

Return to subject

AI TutorYour personal study buddy

Question of the DayDaily practice to build your skills

FlashcardsStudy and memorize key concepts

WorksheetsBuild custom practice quizzes

AI SolverStep-by-step problem solutions

Learn by ConceptMaster concepts step by step

Diagnostic TestsAssess your knowledge level

Practice TestsTest your skills with exam questions

GamesLearn through free games