# Coordinates and Graphs Questions and Answers - Form 1 Topical Mathematics

Questions

1. Find the angle θ in degrees from the figure below
2. In the diagram below, determine the equation of the line XY in the form y = mx + c
3. Find the equation of a line which passes through the point (2, 3) and is perpendicular to y – 3x+ 1 = 0, giving your answer in the form y = mx + c
4. T is the mid-point of line XY where X is point (1,4) and Y is the point (-5, 10). Find the equation of a line, L2 which is perpendicular to line XY and goes through point T
5.
1. On the grid provided below, plot points A(2,1) B(-4,3) and C(2,5)
2. Given that the gradient of CD = -1 and CD =AD locate D and complete the quadrilateral ABCD
3. What name is given to quadrilateral ABCD?
6.  In the figure below (not drawn to scale), PQRS is a rectangle and P and Q are the points (3, 2) and (1,4) respectively.

Given that the equation of the line PQ is y =3x -7, find:
1. The equation of line QR
2. The coordinates of point R
3. The coordinates of point S
7. OABC is a trapezium such that the coordinates of O, A , B and C are (0, 0), (2, -1), (4, 3) and (0, y)
1. Find the value of y
2. M is the mid-point of AB and N is the mid-point of OM. Find in column form
1. the vector AN
2. the vector
3. Vector AC NC
3. Hence show that A, N and C are collinear
8. Use ruler and a pair of compasses only in this question.
1. Construct triangle ABC in which AB = 7 cm, BC = 8 cm and ∠ABC = 600.
2. Measure
1. side AC
2. ∠ ACB
3. Construct a circle passing through the three points A, B and C. Measure the radius of the circle.
4. Construct ∆ PBC such that P is on the same side of BC as point A and ∠ PCB = ½ ∠ ACB, ∠ BPC = ∠ BAC measure ∠ PBC.
9. ABCD is a parallelogram with vertices A (1,1) and C(8,10). AB has the equation 4x -5y = -1 and BC has the equation 5x – 2y = 20. Determine by calculation;
1.  the co-ordinates of the point M where the diagonals meet
2. The co-ordinates of the vertices B and D
3. the length of AB correct to 4 significant figures
10. The table shows corresponding values of x and y for a certain curve;
 x 1 1.2 1.4 1.6 1.8 2 2.3 y 6.5 6.2 5.2 4.3 4 2.6 2.4

Using 3 strips and mid-ordinate rule estimate the area between the curve, x-axis

1. 2x - 3y + 6 =0
-3y = -2x – 6
y = 2x/3 + 2
When y = 0 x = -3
x = 0 y = 2

Co-ordinate of y – intercept is (0,2)
Coordinate of x – intercept is (-3,0)
∴ ∠CAO = tan-1 2/3
= 33.69o
∴∠θ = 180 – 33.69o
= 146.31o
2. Point y(4 + -2/2, 7 + -1/2) = (1, 3)
grad AB = 7 + 1/4 + 2 = 8/6
y – 3/x – 2 = - ¾
y = - ¾ x + 15/4
3.  Y = 3x – 1
M =3
M1M2 = -1
M2 = -1/3
y – 3/x -2= -1/3
3y – 9 =-x +2
3y/3 = -x/3 + 11/3
Y = -x/3 + 11/3
4.  Pt T is 1 + 5/2, 4 + 10/2 = (-2, 7)
grad. of grid xy = 10 - 4/-5 -1 = 14/-6 = -7/-3
∴ grad of L2 = 3/7
Take a general pt P(x,y) on L2
y - 7/x - 2 = 3/7
→7y – 49 = 3x + 6
7y = 3x + 55
Or y = 3x + 55 (equation of L2
5.  a, b

(c) Name : a kite
1. Grad of line QP = 4-2/1-3= 2/-2= -1
Grad of line QR = 1
Take a pt Q(1,4) and T(x,y) on line QR
y- 4/x – 1= 1
y – 4 = x -1
y = x + 3 .....equ. of QR
2. y= x+3 …(i) Equ of QR
y = 3x -7 ...(ii) Equ. of Pr
Solving simultaneously ;:
x +3 = 3x -7
2x = 10
x = 5
Substituting ; y = 8
∴R is the pt (5,8)
3.
-1 – 0/2 – 0 = - ½
y – 3/0 – 4= - ½
2y – 6 = 4
2y = 10
y = 5
2.
3.

4AN = AC And A is a common point hence A, N, C lie on a straight line.
6.

1. ∆ ABC line AB = 7 cm and BC = 8 cm ∡ ABC = 60o
Construction of 60o
2. AC = 7.6 + 0.1 and
ACB = 53 + 1o
3. 2 sides bisector 1
Circle drawn radius 4.4. ± 0.1
4. Bisect ACB
Bisection line to cut the circle to identify P
BPC BAC = 67o
∡ PBC = 88 ± 0.1o
1.

M (1+8/2, 1+10/2) = M (4.5, 5.5)
2. AB: 4x – 5y = -1 x 2
BC: 5x – 2y = 20 x 5
8x – 10y = -2
25x – 10y = 100
-17x = -102
x=102/17 = 6.0
24 – 5y = -1
5y = -25
Y = 5
B(6,5)
x+ 6.0/2 = 4.5 x = 3
y + 5/2 = 5.5 y = 6
D (3,6)
3. AB = √(16 – 1)2 + (5-1)2
√25 + 16
√41 = 6.40 (units)
7. Mid ordinate
Area = 1.2 (6.2 + 4.3 + 2.6)
= 15.72

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