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.

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**Distance Between Two Points**

The formula to find the distance between the two points is usually given by

**d=âˆš((x _{2} â€“ x_{1})Â² + (y_{2} â€“ y_{1})Â²)**.

**Example:** Find the distance between the two points with coordinates given as, A = (1, 2) and B = (1, 5).

**Solution:**

The distance between two points using coordinates can be given as, d = âˆš[(x2 âˆ’ x1)^{2 }+ (y2 âˆ’ y1)^{2}], where (x1,y1) and (x2,y2) are the coordinates of the two points.

â‡’ d = âˆš[(1 âˆ’ 1)^{2} + (5 âˆ’ 2)^{2}]

â‡’ 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 Â· * Its x value is halfway between the two x values* Â· 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.**Â 8 units**B.**Â 11 units**C.**Â 15 units**D.**Â 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.**Â 1**B.**Â 2**C.**Â 3**D.**Â 9

3. The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is

**A.**Â 1/2**B.**Â 2/5**C.**Â âˆ’4/7**D.**Â âˆ’2/3

4. Find the equation of the line through the points (-2, 1) and (-12, 4)

**A.**Â y = 2x – 3**B.**Â y = 2x + 5**C.**Â y = 3x – 2**D.**Â y = 2x + 1

5. If line p = 5x + 3 is parallel to line p = wx + 5. Find the value of w.

**A.**Â 7**B.**Â 3**C.**Â 6**D.**Â 5

**TYPE YOUR ANSWERS INTO THE COMMENT BOX BELOW, THE CORRECTIONS WILL BE POSTED SOON.**