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Analytic Geometry2D

Introduction to Analytic Geometry - Theory & Concepts - Analytic Geometry Distance Slope

Coordinate systems, distance formula, midpoint formula, slope, angle between lines, symmetry, and area of polygons.

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Distance & Slope Explorer

Point 1 (x₁, y₁)

x₁-2
y₁-2

Point 2 (x₂, y₂)

x₂3
y₂4
Distance Formula:
d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
d=(3−(−2))2+(4−(−2))2=(5)2+(6)2≈7.81d = \sqrt{(3 - (-2))^2 + (4 - (-2))^2} = \sqrt{(5)^2 + (6)^2} \approx 7.81
Slope Formula:
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
m=4−(−2)3−(−2)=65≈1.20m = \frac{4 - (-2)}{3 - (-2)} = \frac{6}{5} \approx 1.20
Midpoint Formula:
M=(x1+x22,y1+y22)M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
M=(−2+32,−2+42)=(0.5,1)M = \left(\frac{-2 + 3}{2}, \frac{-2 + 4}{2}\right) = (0.5, 1)
Coordinate system graph displaying distance and slope between two pointsGrid line patternGrid area backgroundX AxisY AxisConnection segment of length 7.81Slope triangle: Run = 5, Rise = 6Midpoint M at (0.5, 1)MPoint 1: (-2, -2)P₁Point 2: (3, 4)P₂

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