**Two-dimensional coordinate geometry:**

Two-dimensional coordinate geometry deals about the coordinates which are represented in a coordinate plane. A coordinate plane has two axes, the one which is horizontal is known as \(X-axis\)

‘\(O\)

The perpendicular distance of \(p(x,y)\)

For example, the point \((2,3)\)

The points having \(x\)

For example, the points \((2,0),(5,0)\)

**Distance between two points:**

Consider two points \(A(x_1,y_1)\)

Then the distance between \(A\)

\(AB\)

For example; distance between the points \(A(2,-3)\)

\( AB\)

Similarly, distance between a point \(P(x,y)\)

\( OP \)

**Reflection of a point across the X-axis**

Reflection of a point \(P(x,y)\)

**Reflection of a point across the Y-axis**

Reflection of a point \(P(x,y)\)

\(x\)

**Section Formula:**

Consider two points \(A(x_1,y_1)\)

\(P(x,y)\)

Then, the \(x\)

\(x\)

the \(y\)

\(y\)

If \( m\)

\((\frac{x_1 ~+~ x_2}{2}, \frac{y_1 ~+ ~y_2}{2}\)

If the point \(P(x,y)\)

Then, the \(x\)

\(x \)

they-coordinate of \(P\)

\(y\)

Example: Find the coordinates of the point which divides the line segment joining \(P(-3,-4)\)

\(Q(6,8)\)

Let \(M(x,y)\)

\(x\)

\(y\)

Therefore origin \((0,0)\)

**Area of a triangle:**

The area of the triangle whose vertices are \((x_1,y_1 ),(x_2,y_2)\)

\(\frac{1}{2}|x_1 (y_2~ -~ y_3)~ + ~x_2(y_3~ – ~y_1)~ +~ x_3(y_1~ – ~y_2)|\)

If the area of a triangle whose vertices are \((x_1,y_1),(x_2,y_2)\)

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