Assignments are more than a routine part of textbook learning. In Class X coordinate geometry they serve several crucial purposes: Students are required to calculate the distance between two points (x, y) and (x, y) using d = [(x x) + (y y)] and to locate the midpoint with M = ((x + x)/2 , (y + y)/2) When a point P divides a line segment joining A(x, y) and B(x, y) in the ratio m:n, the coordinates are P(x, y) = ((mx + nx)/(m+n) , (my + ny)/(m+n)) For external division, the denominator becomes (mn). Assignments often ask students to find the coordinates of points that divide a line segment in a given ratio. The slope (m) between two points is m = (y y)/(x x) Using slopepoint form, the equation of a line passing through (x, y) is y y = m(x x) Assignments often ask for converting between slopeintercept form, pointslope form, and general form Ax + By + C = 0. Two lines are parallel if their slopes are equal (m = m). They are perpendicular if the product of their slopes is 1 (mm = 1). Assignments commonly include questions such as find the equation of a line parallel to 2x 3y + 5 = 0 that passes through (4,2). Most teachers follow a pattern that balances theory, practice, and reflection: Find the equation of the line that passes through the points P(3,4) and Q(2,7). State whether the line is increasing or decreasing. Solution: Slope m = (7 + 4)/(-2 3) = 11/5 = -2.2 (negative decreasing). Using P(3,4): y + 4 = -2.2(x 3) y = -2.2x + 6.6 4 y = -2.2x + 2.6. A road segment AB has end points A(0,0) and B(12,16). A surveillance camera is to be installed at a point that divides AB in the ratio 3:5 (measured from A). Find the coordinates of the camera location. Solution: Using internal section formula: x = (312 + 50)/(3+5) = 36/8 = 4.5; y = (316 + 50)/8 = 48/8 = 6. So the camera should be placed at (4.5,6). Determine the perpendicular distance of the point R(5,9) from the line 4x + 3y 7 = 0. Formula: Distance = |Ax + By + C| / (A + B). The board exam includes a section on coordinate geometry. To be fully prepared, students should: For further practice and concept clarification, consider the following online resources:Assignments in Mathematics Class X Coordinate Geometry
Why Assignments Matter
Key Topics Covered in Typical Assignments
1. Distance and Midpoint Formula
Example: Find the distance and midpoint of A(2, 3) and B(8, 5).
Solution: d = [(82) + (5+3)] = [36 + 64] = 100 = 10.
M = ((2+8)/2 , (3+5)/2) = (5 , 1). 2. Section Formula (Internal & External)
Example: Find the point dividing AB, where A(1,2) and B(7,8), in the ratio 3:2 internally.
Solution: x = (37 + 21)/(3+2) = (21+2)/5 = 23/5 = 4.6
y = (38 + 22)/5 = (24+4)/5 = 28/5 = 5.6 3. Slope of a Line & Equation of a Straight Line
Example: Find the equation of the line passing through (2, 5) with slope 3.
Solution: y 5 = 3(x + 2) y = 3x 6 + 5 y = 3x 1. 4. Perpendicular and Parallel Lines
Solution: 2x 3y + 5 = 0 3y = 2x + 5 y = (2/3)x + 5/3, so slope = 2/3. Parallel line: slope = 2/3. Using pointslope:
y + 2 = (2/3)(x 4) 3(y + 2) = 2(x 4) 3y + 6 = 2x 8 2x 3y 14 = 0. Typical Assignment Structure
Tips for Completing Assignments Efficiently
Read the question twice. The first reading helps you identify what is being asked; the second lets you spot hidden data. Sketch a diagram. Even a quick sketch often reveals relationships between points and lines that are not obvious from text alone. List known formulas. Having the distance, midpoint, and slope formulas in front of you reduces the chance of algebraic slip. Check units and signs. Coordinate geometry problems frequently involve negative coordinates; a missed sign can change the answer entirely. Verify by substitution. Insert the coordinates you obtained back into the original line equation to confirm correctness. Sample Assignment (FullLength)
Problem 1
Problem 2
Problem 3
Solution: |4(5) + 39 7| / (4 + 3) = |20 + 27 7| / (16 + 9) = |0| / 25 = 0.
Therefore, R lies on the line.Preparing for the Board Examination
Additional Resources
