Coordinate geometry and slope — SSAT Upper practice questions

102 practice questions in the app
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Practice 102 Coordinate geometry and slope questions in the app

What this topic is

Coordinate geometry and slope questions place points on a grid and ask about distances, slopes and areas.

Slope is the change in y divided by the change in x, often called rise over run, and subtracting in a different order on the top and bottom flips its sign. Two points with the same y-coordinate lie on a horizontal line, so their distance is simply the difference of their x-coordinates; otherwise the Pythagorean theorem gives it.

Area items often use a triangle with a horizontal or vertical side as its base, which makes the height easy to read. Expect SSAT Upper choices to include the negative of the right answer.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

Points $A (2, 5)$ and $B (8, 5)$ are on a coordinate plane. What is the distance from $A$ to $B$ ?

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Answer: A — 6

The horizontal distance is the difference in $x$ -coordinates: $8 - 2 = 6$ .

Question 2Mid

In the coordinate plane, points $A (1, 2)$ , $B (9, 2)$ , and $C (9, 8)$ are vertices of triangle $A B C$ . Point $D$ lies on segment $A B$ . If the area of triangle $D B C$ is 18 square units, what is the $x$ -coordinate of $D$ ?

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Answer: B — 3

The height from $C$ to line $A B$ is $8 - 2 = 6$ . If $D$ has $x$ -coordinate $d$ , then $D B = 9 - d$ . The area equation is $\frac{1}{2} (9 - d) (6) = 18$ , so $d = 3$ .

Question 3Harder

A line with slope $- \frac{3}{4}$ contains the points $(- 2, 7)$ and $(6, t)$ . What is the value of $t$ ?

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Answer: B — 1

Use $\frac{t - 7}{6 - (- 2)} = - \frac{3}{4}$ . Then $\frac{t - 7}{8} = - \frac{3}{4}$ , so $t - 7 = - 6$ and $t = 1$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 102 Coordinate geometry and slope questions in the app

Coordinate geometry and slope — SSAT Upper practice questions

What this topic is

Sample questions

More SSAT Upper topics

Quantitative (Math)