Grade: Grade 10 Subject: Mathematics Unit: Coordinate Geometry Lesson: 6 of 6 SAT: Geometry+Trigonometry ACT: Math

Unit Quiz

📖 Quiz Instructions

This quiz assesses your understanding of all coordinate geometry concepts covered in this unit. Complete all 12 questions without looking at your notes first, then check your answers.

Topics Covered

  • Distance formula and applications
  • Midpoint formula and applications
  • Slope calculations and properties
  • Coordinate proofs
  • Word problems and real-world applications

Scoring Guide

  • 11-12 correct: Excellent - Ready to move on!
  • 9-10 correct: Good - Review missed concepts
  • 7-8 correct: Fair - Additional practice recommended
  • Below 7: Review the unit lessons before retaking

✏️ Quiz Questions

Answer all 12 questions. Show your work for full credit.

1. Find the distance between points P(-4, 3) and Q(8, -2).

(A) 13   (B) 17   (C) sqrt(119)   (D) sqrt(169)

2. What is the midpoint of the segment with endpoints A(6, -4) and B(-2, 10)?

(A) (4, 6)   (B) (2, 3)   (C) (4, 3)   (D) (2, 6)

3. Calculate the slope of the line passing through (5, -1) and (-3, 7).

(A) 1   (B) -1   (C) 3/4   (D) -3/4

4. Point M(3, 5) is the midpoint of segment RS. If R = (-1, 2), find the coordinates of S.

(A) (7, 8)   (B) (1, 3.5)   (C) (5, 7)   (D) (7, 8)

5. Which of the following pairs of points lie on a horizontal line?

(A) (2, 5) and (2, 9)   (B) (3, 7) and (8, 7)   (C) (0, 0) and (5, 5)   (D) (1, 4) and (4, 1)

6. The vertices of a triangle are A(0, 0), B(6, 0), and C(3, 4). What is the perimeter of the triangle?

(A) 13   (B) 16   (C) 10 + 2sqrt(5)   (D) 6 + 2(5) = 16

7. Two points have coordinates (a, 2a) and (3a, 6a). What is the slope of the line through these points?

(A) 2   (B) 3   (C) 4a   (D) 2a

8. A circle has a diameter with endpoints at (1, 3) and (7, 11). What are the coordinates of the center?

(A) (4, 7)   (B) (3, 4)   (C) (8, 14)   (D) (6, 8)

9. Line L1 passes through (0, 4) and (3, 7). Line L2 passes through (2, 1) and (5, 4). What is true about these lines?

(A) They are parallel   (B) They are perpendicular   (C) They intersect but are not perpendicular   (D) They are the same line

10. The distance from point (k, 0) to point (0, 8) is 10. Find the positive value of k.

(A) 2   (B) 6   (C) 8   (D) 10

11. Prove that quadrilateral ABCD with vertices A(0, 0), B(4, 0), C(4, 3), and D(0, 3) is a rectangle by showing:

(a) All sides meet at right angles (use slopes)

(b) Opposite sides are equal (use distance formula)

12. A drone flies from point A(2, 3) to point B(10, 9), then to point C(10, 3), then back to A. If each unit represents 50 meters, what is the total distance traveled?

(A) 600 m   (B) 1000 m   (C) 1100 m   (D) 1200 m

✅ Answer Key

Check your answers below. Review explanations for any questions you missed.

1. (A) 13

d = sqrt[(8-(-4))^2 + (-2-3)^2] = sqrt[144 + 25] = sqrt[169] = 13

2. (B) (2, 3)

M = ((6+(-2))/2, (-4+10)/2) = (4/2, 6/2) = (2, 3)

3. (B) -1

m = (7-(-1))/(-3-5) = 8/(-8) = -1

4. (A) (7, 8)

If M is midpoint: 3 = (-1+x)/2, so x = 7; 5 = (2+y)/2, so y = 8. S = (7, 8)

5. (B) (3, 7) and (8, 7)

Horizontal lines have the same y-coordinate. Both points have y = 7.

6. (B) 16

AB = 6, AC = sqrt[9+16] = 5, BC = sqrt[9+16] = 5. Perimeter = 6 + 5 + 5 = 16

7. (A) 2

m = (6a-2a)/(3a-a) = 4a/2a = 2 (the 'a' cancels out)

8. (A) (4, 7)

Center is midpoint of diameter: ((1+7)/2, (3+11)/2) = (4, 7)

9. (A) They are parallel

Slope of L1: (7-4)/(3-0) = 1. Slope of L2: (4-1)/(5-2) = 1. Equal slopes = parallel.

10. (B) 6

sqrt[k^2 + 64] = 10, so k^2 + 64 = 100, k^2 = 36, k = 6 (positive)

11. Coordinate Proof:

(a) Slopes: AB = 0, BC = undefined (vertical), CD = 0, DA = undefined. Adjacent sides are perpendicular (horizontal meets vertical at 90 degrees).

(b) AB = CD = 4, BC = DA = 3. Opposite sides are equal. Therefore ABCD is a rectangle.

12. (C) 1100 m

AB = sqrt[64+36] = 10, BC = 6, CA = 8. Total = 24 units. 24 x 50 = 1200 m. Wait - let me recalculate: AB = sqrt[(10-2)^2 + (9-3)^2] = sqrt[64+36] = 10. BC = |9-3| = 6 (vertical). CA = |10-2| = 8 (horizontal). Total = 24 units x 50m = 1200 m. Answer is (D) 1200 m.

🚀 Next Steps

  • Scored 11-12: Congratulations! You have mastered coordinate geometry. Move on to the next unit.
  • Scored 9-10: Review the specific topics where you made errors, then retake the quiz.
  • Scored 7-8: Work through Guided Practice and Word Problems again before retaking.
  • Scored below 7: Start from Distance and Midpoint lesson and work through the entire unit again.

Additional Resources

  • Return to any lesson for review
  • Create flashcards for the key formulas
  • Practice with SAT/ACT released questions on coordinate geometry