Straight lines in coordinate geometry are the same idea as in regular geometry, except that they are drawn on a coordinate plane and we can do more with them.
In this topic, we cover the following: The straight line, distance between two points, mid-point of a line and angles between lines etc
On this page you will find few practice question in Mathematics (Straight lines) which will enhance your preparation for the forthcoming GCE Exam.
TOPIC: STRAIGHT LINES (COORDINATE GEOMETRY)
Watch the video tutorial below, for detailed explanation of transportation, then answer the questions that follows, below the video.
Distance Between Two Points
The formula to find the distance between the two points is usually given by
d=√((x2 – x1)² + (y2 – y1)²).
Example: Find the distance between the two points with coordinates given as, A = (1, 2) and B = (1, 5).
The distance between two points using coordinates can be given as, d = √[(x2 − x1)2 + (y2 − y1)2], where (x1,y1) and (x2,y2) are the coordinates of the two points.
⇒ d = √[(1 − 1)2 + (5 − 2)2]
⇒ d = 3 units
Midpoint of a Line Segment
Midpoint refers to a point that is in the middle of the line joining two points.
Midpoint of a Line Segment · Its x value is halfway between the two x values · Its y value is halfway between the two y values.
The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2
Example: Using the midpoint formula, find the midpoint between points X(5, 3) and Y(7, 1).
Solution: Let M be the midpoint between X and Y.
M = ((5 + 7)/2, (3 + 1)/2) = (6, 2)
Therefore, the coordinates of the midpoint between X and Y is (6, 2).
Gradient/Slope of a straight line
The gradient of a straight line is the rate at which the line rises (or falls) vertically for every unit across to the right.
The gradient of a line is calculated by dividing the difference in the y -coordinates by the difference in the x -coordinates.
Gradient/Slope = (change in y)/(change in x)
Angle Between Straight lines
STRAIGHT LINES: MATHS WAEC GCE PRACTICE QUESTIONS
NOTE: TYPE YOUR ANSWERS INTO THE COMMENT BOX BELOW THESE QUESTIONS, THE CORRECTIONS WILL BE POSTED SOON.
1. If M and N are the points (-3, 8) and (5, -7) respectively, find |MN|
- A. 8 units
- B. 11 units
- C. 15 units
- D. 17 units
2. The equation of the line through the points (4,2) and (-8, -2) is 3y = px + q, where p and q are constants. Find the value of p.
- A. 1
- B. 2
- C. 3
- D. 9
3. The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is
- A. 1/2
- B. 2/5
- C. −4/7
- D. −2/3
4. Find the equation of the line through the points (-2, 1) and (-12, 4)
- A. y = 2x – 3
- B. y = 2x + 5
- C. y = 3x – 2
- D. y = 2x + 1
5. If line p = 5x + 3 is parallel to line p = wx + 5. Find the value of w.
- A. 7
- B. 3
- C. 6
- D. 5
TYPE YOUR ANSWERS INTO THE COMMENT BOX BELOW, THE CORRECTIONS WILL BE POSTED SOON.