Grade: Grade 10 Subject: Mathematics Unit: Coordinate Geometry Lesson: 3 of 6 SAT: Geometry+Trigonometry ACT: Math

Guided Practice

📖 Learn

This lesson provides guided practice to reinforce your understanding of coordinate geometry fundamentals. You will work through problems step-by-step, building confidence with the distance formula, midpoint formula, and slope calculations.

Key Formulas Review

Distance Formula: d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Midpoint Formula: M = ((x1 + x2)/2, (y1 + y2)/2)

Slope Formula: m = (y2 - y1)/(x2 - x1)

Problem-Solving Strategy

  1. Identify what the problem is asking (distance, midpoint, or slope)
  2. Extract the coordinates from the problem
  3. Label your points as (x1, y1) and (x2, y2)
  4. Substitute values into the appropriate formula
  5. Simplify and check your answer

💡 Examples

Work through these guided examples to see the problem-solving process in action.

Example 1: Finding Distance

Problem: Find the distance between A(2, 3) and B(8, 11).

Solution:

  1. Identify: We need the distance between two points
  2. Label: (x1, y1) = (2, 3) and (x2, y2) = (8, 11)
  3. Substitute: d = sqrt[(8-2)^2 + (11-3)^2]
  4. Simplify: d = sqrt[36 + 64] = sqrt[100] = 10 units

Example 2: Finding Midpoint

Problem: Find the midpoint of the segment connecting P(-4, 6) and Q(10, -2).

Solution:

  1. Identify: We need the midpoint of a segment
  2. Label: (x1, y1) = (-4, 6) and (x2, y2) = (10, -2)
  3. Substitute: M = ((-4+10)/2, (6+(-2))/2)
  4. Simplify: M = (6/2, 4/2) = (3, 2)

Example 3: Finding Slope

Problem: Find the slope of the line through R(1, -5) and S(4, 7).

Solution:

  1. Identify: We need the slope of a line
  2. Label: (x1, y1) = (1, -5) and (x2, y2) = (4, 7)
  3. Substitute: m = (7 - (-5))/(4 - 1)
  4. Simplify: m = 12/3 = 4

✏️ Practice

Try these 10 problems on your own. Work through each step carefully.

1. Find the distance between (0, 0) and (5, 12).

2. Find the midpoint of the segment with endpoints (2, 8) and (6, 4).

3. Calculate the slope of the line through (-3, 2) and (5, 10).

4. Find the distance between A(-2, -3) and B(4, 5).

5. Point M is the midpoint of segment PQ. If P = (1, 7) and M = (4, 3), find Q.

6. Determine if points A(1, 1), B(4, 5), and C(7, 9) are collinear by comparing slopes.

7. Find the perimeter of triangle DEF with vertices D(0, 0), E(6, 0), and F(3, 4).

8. The endpoints of a diameter of a circle are (2, -1) and (8, 7). Find the center and radius.

9. Find the distance from the origin to the point (7, -24).

10. A line passes through (2, k) and (5, 9) with slope 2. Find k.

✅ Check Your Understanding

Verify your answers to the practice problems.

1. 13 units

2. (4, 6)

3. m = 1

4. 10 units

5. Q = (7, -1)

6. Yes, collinear (both slopes = 4/3)

7. 16 units (6 + 5 + 5)

8. Center: (5, 3), Radius: 5

9. 25 units

10. k = 3

🚀 Next Steps

  • If you scored 8/10 or higher, proceed to Word Problems
  • If you scored below 8/10, review the formulas and try similar problems
  • Practice identifying which formula to use before calculating
  • Create your own problems using coordinates from a graph