Chapter 3 · Class 10 ICSE · Formula Sheet
Coordinate Geometry Formulas — Class 10 ICSE
Find distance, midpoint, section formula, and slope of lines in the coordinate plane.
Key Formulas
Distance Formula
d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
Section Formula
\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)
Midpoint
M = \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)
Slope
m = \dfrac{y_2-y_1}{x_2-x_1}
Slope-Intercept Form
y = mx + c
Point-Slope Form
y - y_1 = m(x - x_1)
Parallel Lines
m_1 = m_2
Perpendicular Lines
m_1 \times m_2 = -1
Worked Examples
1Using: Supplementary Angles
If one angle is 65 degrees, find its supplement.
Step 1: Supplement = 180 - 65
Step 2: = 115 degrees.
Answer: 115 degrees
2Using: Vertically Opposite
Two lines intersect. If one angle is 40 degrees, find the vertically opposite angle.
Step 1: Vertically opposite angles are equal.
Step 2: The angle = 40 degrees.
Answer: 40 degrees
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