📝 Coordinate Geometry
● The distance of a point from the `y`-axis is called its `x`-coordinate, or abscissa.
● The distance of a point from the `x`-axis is called its `y`-coordinate, or ordinate.
● The coordinates of a point on the `x`-axis are of the form `(x, 0)`, and of a point on the `y`-axis are of the form `(0, y)`.
Distance Formula
● The distance between `P(x_1, y_1)` and `Q(x_2, y_2)` is `\sqrt {(x_2 - x_1)^2 + (y_2 -y_1)^2}`
● The distance of a point `P(x, y)` from the origin is `\sqrt {x^2 + y^2}`
Section Formula
● The coordinates of the point `P(x, y)` which divides the line segment joining the points `A(x_1, y_1)` and `B(x_2, y_2)` internally in the ratio `m_1 : m_2` are
`(\frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2})`
● The mid-point of the line segment joining the points `P(x_1, y_1)` and `Q(x_2, y_2)` is
`(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})`
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Area of a Triangle
● The area of the triangle formed by the points `(x_1, y_1), (x_2, y_2)` and `(x_3, y_3)` is the numerical value of the expression
`1/2[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)`