How to find the points on a coordinate plane - SSAT Middle Level Math

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Question

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

Answer

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

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Question

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

Answer

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.

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Question

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

Answer

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 .

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Question

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

Answer

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.

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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.

Answer

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 .

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Question

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.

Answer

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

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