📘 coordinate geometry

1. **Problem:** Find the coordinates of point C such that $AC = 2BC$ where $A=(-3,4)$ and $B=(2,1)$. 2. **Formula:** If $C$ divides the segment $AB$ in the ratio $m:n$, then coordi

1. **Problem Statement:** Find the equation of the line through the midpoint of segment AB that is perpendicular to AB, where A(-2, -3) and B(4, 9). Then use this to find the coord

1. The problem asks to select the point (-5,1) on the coordinate plane. 2. The coordinates (-5,1) mean 5 units to the left of the origin (0,0) and 1 unit up.

1. The problem asks to select the point with coordinates $x=4$ and $y=2$ on the coordinate plane. 2. Points are identified by their $(x,y)$ coordinates, where $x$ is the horizontal

1. The problem is to graph the point $(-1, 2.5)$ on the coordinate plane. 2. The coordinate plane has two axes: the horizontal axis is the $x$-axis and the vertical axis is the $y$

1. **State the problem:** We are given points C(6,0), D(0,-3), E(-2,0), H(-1,-5), and I(-3,2). We need to list each ordered pair and identify which quadrant or axis each point lies

1. **State the problem:** Find the equation of the line AB given points A(-1, 3) and B(5, 6), and find the coordinates of point P that divides AB in the ratio 2:1. 2. **Find the eq

1. **State the problem:** We have points A(0,5), B(-4,0), and C(4,0) representing parts of a swing frame. We need to find:

1. The problem asks to plot the point $\left(-\frac{1}{2}, \frac{1}{2}\right)$ on the coordinate axes. 2. The coordinate $\left(x, y\right)$ means move $x$ units along the horizont

1. The problem is to create a sample C1 (Coordinate Geometry) question for Sec 3 math midterm in Montreal. 2. A typical C1 problem involves finding the equation of a line, distance

1. **Nyatakan masalah:** Cari persamaan lokus titik P yang jaraknya dari A adalah dua kali jaraknya dari B. 2. **Diberi:** Titik A(-3, 4) dan titik B(6, -2).

1. Problem 8: Find $m\angle K$. 2. Problem 9: Find $m\angle Q$.

1. The user requests a 100-mark mathematics test paper for O Level students on coordinate geometry, all types of graphs (excluding modulus graphs), and functions. 2. Creating a ful

1. **Problem Statement:** Given two vertices of an equilateral triangle at points $(-5,3)$ and $(5,3)$, find the coordinates of the third vertex such that the origin $(0,0)$ lies i

1. **Problem Statement:** Prove that if $p$ and $q$ are the lengths of the perpendiculars from the origin to the lines

1. **Problem statement:** Find the ratio in which the line $2x + y - 4 = 0$ divides the line segment joining points $A(2, -2)$ and $B(3, 7)$. 2. **Formula used:** If a point $P$ di

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