📘 coordinate geometry

1. **State the problem:** (a) Find the value of $h$ if point $P(h,7)$ lies on the line $3y + 2x = 5$.

1. **Problem statement:** Find the coordinates of point B given that point P(3, 5) divides the line segment joining A(2, 4) and B in the ratio 1:1 internally. 2. **Formula used:**

1. **Problem statement:** Find the coordinates of point C that divides the line segment AB externally in the ratio $|AC| : |CB| = 4 : 1$, where $A=(-2,-1)$ and $B=(3,4)$. 2. **Form

1. Problem statement: Find the ordinate of the point $ (5,9) $. 2. Formula used: For any ordered pair $ (x,y) $, the ordinate is the second coordinate $y$.

1. **Problem:** Find the coordinates of point D that divides the segment RS externally in the ratio 4:1, where R(2, 3) and S(8, 9). 2. **Formula:** For external division of a segme

1. **State the problem:** We have a parallelogram PARM with points P(2,9), R(n,-13), T(10,-3), and M the midpoint of PT. We need to find: 3.1.1 The length of PT in surd form.

1. Given points A(-2t, h), B(pt, t), and C(2p, 2t) lie on a straight line, and B divides AC such that $AB = \frac{1}{3} AC$. 2. To find $p$ in terms of $h$, use the section formula

1. Check whether the pairs of lines are parallel. (i) Lines: $2y - 6x - 1 = 0$ and $4y = 12x - 1$

1. **Problem Statement:** Find the ratio in which the line segment joining points $A(-2,-3)$ and $B(5,6)$ is divided by (i) the x-axis and (ii) the y-axis. Also, find the coordinat

1. **Problem Statement:** Find the equation of the straight line passing through each pair of points given. 2. **Formula:** The equation of a line through points $(x_1, y_1)$ and $

1. Let's start by understanding that coordinate geometry involves points, lines, and shapes in the coordinate plane. 2. A common problem is finding the distance between two points

1. The point (0, -2) has $x=0$ and $y=-2$. Since $x=0$, it lies on the y-axis. Because $y$ is negative, it lies on the negative direction of the y-axis. So, the answer is (b). 2. A

1. **Problem:** Which expression represents the distance $d$ between the two points $(x_1,y_1)$ and $(x_2,y_2)$? 1. **Solution:** The horizontal change is $\Delta x = x_2 - x_1$.

1. We are given points A(11,-2), B(3,6), and a point P(a,3) on the line joining A and B. 2. We want to find the ratio in which P divides AB and also the value of a.

1. The problem asks to determine the direction in which the parabola $x=4y^2$ opens. 2. Rewrite the equation: $x=4y^2$ can be compared to the standard form of a parabola that opens

1. Problem: Find the distance between the points $A(3,4)$ and $B(7,1)$.\n\n2. Step 1: Use the distance formula between two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$:

1. **State the problem:** We need to find the midpoint between two points on a coordinate plane, which represents the location of the carousel. 2. **Given points:** Ferris wheel at