Question 1Mid
Line passes through and . Which point lies on a line perpendicular to that passes through ?
Show answer
Answer: D —
The slope of is . A perpendicular line has slope . From to , the slope is , so lies on the perpendicular line.
Study on the flyISEE UpperMathematics AchievementCoordinate geometry (midpoint, distance)
Mathematics Achievement
Coordinate geometry (midpoint, distance) — ISEE Upper practice questions
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What this topic is
Coordinate geometry (midpoint, distance) uses two formulas built on simple ideas.
The midpoint is the average of the x-coordinates paired with the average of the y-coordinates. Distance comes from the Pythagorean theorem, though points sharing an x-value are simply apart by the difference of their y-values. Reflections are also tested: reflecting across the x-axis keeps x and changes the sign of y, while reflecting across the y-axis does the opposite, and the swapped version is usually a choice.
Some questions add slope, asking for a point on a line perpendicular to a given one, which uses the negative reciprocal slope.
Sample questions
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 2Easier
What is the reflection of across the -axis?
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Answer: B —
Reflection over the -axis keeps x and negates y, producing .
Question 3Easier
What is the vertical distance between and ?
Show answer
Answer: B — 6
The x-coordinates match, so distance is .
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
Practice 89 Coordinate geometry (midpoint, distance) questions in the app
More ISEE Upper topics
Mathematics Achievement
- Numbers and operations (factors, multiples, properties)
- Fractions, decimals, and percents; percent change
- Ratios and proportions; distance-rate-time
- Exponents, powers, roots; scientific notation
- Algebraic expressions and solving equations
- Inequalities
- Linear equations and graphs
- Polynomials and function notation
- Plane geometry (polygons, triangles, angles)
- Solid geometry (surface area, volume)
- Trigonometry
- Measurement and units
- Data analysis and probability
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