Questions on Coordinate Geometry

What is Co-ordinate Geometry?

Co-ordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates. (kindly use the comment box below to ask a question).

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Questions on Co-ordinate Geometry

1. Find the gradient of a line that passes through the following points.

• A(3,-2) ;  B(-6,-7)
• A(1,4)   ;  B(5,12)
• A(-5,-12)  ;  B(2,3)

 

2. Find the distance between the following pairs of points.

• (2,3)    and  (-2,-2)
• (-2,-3) and  (-6,-8)
• (1,5)    and   (7,3)

 

3. Find the co-ordinates of the point which divides the following lines in the given ratio:

• (3,4)   ;  (5,6)  into ratio  3:4
• (2,-7) ;  (7,3)  into ratio  1:2
• (1,2)   ;  (6,5)  into ratio  2:1

 

4. A point P(x,y) divides the line joining the points (1,-2) and (3,5) into the ratio 1:4. What are the co-ordinates of P?

 

5. Find the co-ordinates of the mid-point of the following:

• (3,4)   ;  (5,6)
• (2,-7) ;  (7,3)
• (1,2)   ;  (6,5)

 

6. A, B, C are three points with coordinates (1,0) ; (2,-4) and (-5,-2) respectively. Determine:

• The equation of the line through A and perpendicular to BC
• The equation of the line through B and perpendicular to AC
• The co-ordinate of the point of intersection of these lines.

 

7. A car hire company estimates that the cost of acquiring and operating a car hire can be estimated by the linear equation:

Y = 0.71x + 1800

Where y represents the total cost (in Naira), and x represents the number of kilometers driven.

• Identify the gradient and y-intercepts.
• Interpret the meaning of the gradient and the y-intercept.

 

8. The bottling company produces 200 crates of Viju for N6,000 and 500 crates for N9,000. If the cost function is linear. Find:

• The cost equation.
• The overhead cost.
• Sketch the graph.
• Estimate the cost of producing 1000 crates.
• The average cost of producing 1,000 crates.

 

9. A company produces 2,000 units of a good for N6,000 and 4,000 units for N10,000. Given that the cost function is linear.

• Find the cost equation.
• Sketch the graph.
• Interpret the slope and the intercept.
• Estimate the cost of producing 7,000 units of the good.
• Find the average cost of producing 7,000 units of goods.

 

10. The additional cost of producing each unit of a certain good is N0.95. If 300 units of the goods are produced at a cost of N8,560. Find:

• The cost equation.
• The overhead cost.
• Sketch the graph.
• The average cost.

Other Mathematics Questions

1. Linear Programming
2. Permutation and Combination
3. Set Theory
4. Empirical Probability
5. Integration & Vector Algebra
6. Differentiation

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