Coordinate Geometry

### Find the distance of each of the following points from the origin: (i) (ii)

(i) $\mathrm{A}(5,-12)$ Let $A(0,0)$ be the origin $$&A=\sqrt{(5-0)^{2}+(-12-0)^{2}}\\$$  \begin{aligned} &=\sqrt{(5)^{2}+(-12)^{2}} \\ &=\sqrt{25+144} \\ &=\sqrt{169} \\ &=13 \text { units }...

### Find the distance between the points (iii) and (iv) and

(iii) $\mathrm{A}(-6,-4)$ and $\mathrm{B}(9,-12)$ points are $\mathrm{A}(-6,-4)$ and $\mathrm{B}(9,-12)$ => $\left(x_{1}=-6, y_{1}=-4\right)$ and $\left(x_{2}=9, y_{2}=-12\right)$...

### State whether the following statements are true or false. Justify your answer. Point P (β 4, 2) lies on the line segment joining the points A (β 4, 6) and B (β 4, β 6).

Solution: The statement given in the question is true. Justification: Equation of the line conatining the points A and B using the two-point form is, $\frac{y-6}{x+4}=\frac{-6-6}{-4+4}$...

### Find the point on the x-axis which is equidistant from (2, β 5) and (- 2, 9).

Solution: To locate a point on the x-axis. As a result, its y-coordinate will be zero. Let's say the x-axis point is (x,0). Consider the following : A = (x, 0), B = (2, β 5), and C = (- 2, 9)....

### Find the distance between the following pairs of points:

(i) (a, b), (- a, β b) Solution: (i) Distance between (a, b), (-a, -b) $d=\sqrt{{{\left( -a-a \right)}^{2}}+{{\left( -b-b \right)}^{2}}}=\sqrt{{{\left( -2a \right)}^{2}}+{{\left( -2b \right)}^{2}}}$...