Coordinate geometry and slope — SSAT Upper practice questions

Coordinate geometry and slope on the SSAT Upper Quantitative (Math) section covers points on a coordinate plane, distances between them, figures built from given vertices, and lines whose slope is known. A student has to find a distance, locate a point from an area condition, and use the slope formula to solve for a missing coordinate. Questions typically give labeled points and ask for a length, an x-coordinate, or an unknown y-value. Answer choices are numbers, sometimes fractions. Common traps are swapping rise and run, mixing which points belong to which segment, and treating a horizontal line as if its slope were not zero.

Section: Quantitative (Math) 50 questions on the paper
91 practice questions in the app

Sample questions

Question 1

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 2

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

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Answer: B — 3

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

Question 3

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

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Answer: B — 1

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

Practice 91 Coordinate geometry and slope questions in the app

Coordinate geometry and slope — SSAT Upper practice questions

Sample questions

More SSAT Upper topics

Quantitative (Math)