Coordinate Geometry

Topics in this chapter

• Coordinate Plane Basics
• Distance And Section Formulas
• Slope And Collinearity
• Area, Centroid And Triangles
• Quadrilaterals And Coordinate Properties
• Coordinate Geometry Of Circles

Cheat sheet

Practice questions

1. Question 1Q-8A9C01

   What is the distance of the point $P(-6, 8)$ from the origin?

   1. A.$6$ units
   2. B.$8$ units
   3. C.$10$ units
   4. D.$14$ units
   See the answer and solution
2. Question 2Q-C18CC6

   Find the coordinates of the point which divides the join of $(-1, 7)$ and $(4, -3)$ in the ratio $2:3$.

   1. A.$(1, 3)$
   2. B.$(2, 2)$
   3. C.$(-1, 3)$
   4. D.$(3, 5)$
   See the answer and solution
3. Question 3Q-AE29A5

   If the points $A(1, 2)$, $O(0, 0)$, and $C(a, b)$ are collinear, then which of the following relations is true?

   1. A.$a + b = 0$
   2. B.$2a = b$
   3. C.$a = 2b$
   4. D.$a = b$
   See the answer and solution
4. Question 4Q-601B20

   If the distance between the points $(x, -1)$ and $(3, 2)$ is $5$ units, find the positive value of $x$.

   1. A.$7$
   2. B.$-1$
   3. C.$3$
   4. D.$5$
   See the answer and solution
5. Question 5Q-EF50CE

   The vertices of a triangle are $(1, K)$, $(4, -3)$, and $(-9, 7)$. If its area is $15$ square units, find the possible values of $K$.

   1. A.$3$ or $-9$
   2. B.$-3$ or $9$
   3. C.$2$ or $-2$
   4. D.$1$ or $-1$
   See the answer and solution