Joining (1, 2) to (3, 8) gives a gradient of 3 and the midpoint of (2, 3) and (6, 7) is (4, 5), so gradients and midpoints open this Year 12 coordinate sheet. The key also records y = 2x + 3 for a line and −⅓ for a perpendicular gradient.
Key Takeaways
The gradient joining (1, 2) and (3, 8) is 3 (Q1).
The midpoint of (2, 3) and (6, 7) is (4, 5) (Q2).
The key records y = 2x + 3 and a perpendicular gradient of −⅓.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The gradient of the line joining (1, 2) and (3, 8) is:
(a) 3(b) 6(c) 2(d) 5
2.The midpoint of the points (2, 3) and (6, 7) is:
(a) (4, 5)(b) (3, 4)(c) (8, 10)(d) (2, 4)
3.The line through (0, 3) with gradient 2 has equation:
(a) y = 2x + 3(b) y = 3x + 2(c) y = 2x − 3(d) y = x + 3
4.The gradient of a line perpendicular to y = 3x − 1 is:
(a) −⅓(b) 3(c) −3(d) ⅓
5.The circle with equation x² + y² = 25 has radius:
(a) 5(b) 25(c) 10(d) √5
6.The distance between the points (1, 1) and (4, 5) is:
(a) 5(b) 7(c) √10(d) 4
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Find the equation of the line through (1, 2) and (3, 6).
8.Find the equation of the line through (0, 4) perpendicular to y = 2x + 1.
9.Find the midpoint of the points (4, −2) and (6, 8).
10.Write down the centre and radius of the circle (x − 2)² + (y + 1)² = 9.
11.Find the gradient of the line 3x + 4y = 12.
12.The line through (1, 3) and (4, k) has gradient 2. Find k.
13.Find the equation of the line perpendicular to y = x + 2 that passes through (3, 1).
14.Show that the lines y = 2x + 1 and 6x − 3y + 5 = 0 are parallel.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Points A(−2, 1) and B(4, 9) are the endpoints of a diameter of a circle. Find the centre and the radius of the circle.
16.A point P lies on the segment joining (2, 0) and (8, 0). P is twice as far from (8, 0) as from (2, 0). Find the coordinates of P.
17.A triangular plot has vertices at (0, 0), (6, 0) and (3, 6). Find its area.
18.A circle has centre (0, 0) and passes through the point (3, 4). Find the equation of the circle.
19.The line y = 2x − 3 passes through the point (a, 7). Find the value of a.
20.A straight road runs from (1, 2) to (5, 10). Find the gradient of the road and write down the equation of the road.
Answer Key
1. a) 3
2. a) (4, 5)
3. a) y = 2x + 3
4. a) −⅓
5. a) 5
6. a) 5
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the gradient of the line joining (1, 2) and (3, 8)?
3, option (a) in this worksheet (Q1).
What is the midpoint of (2, 3) and (6, 7)?
(4, 5), option (a) in this worksheet (Q2).
What gradient is perpendicular to 3?
−⅓, from the answer key on this page.
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