Coordinates Geometry_P_1
1a. [2 marks]
Line L1 passes through the points A(−3, 0.5) and B(9, −3.5).
Find the gradient of L1.
1b. [2 marks]
Line L2 passes through the point C(3, 1) and is parallel to L1.
Determine the equation of L2. Give your answer in the form , where , and are
integers.
1c. [2 marks]
Find the coordinates of the -intercept of L2.
2a. [2 marks]
Line has a -intercept at (0, 3) and an -intercept at (4, 0), as shown on the following diagram.
Find the gradient of .
2b. [1 mark]
Write down the equation of in the form .
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2c. [1 mark]
Line is perpendicular to , and passes through point P(2, 1).
Write down the gradient of .
2d. [2 marks]
Find the equation of in the form .
3a. [2 marks]
The diagram shows a triangle defined by the points A(3 , 9), B(15 , 6) and C(5 , 3).
Calculate the gradient of the line AC.
3b. [2 marks]
Determine, giving a reason, whether angle AĈ B is a right angle.
3c. [2 marks]
The straight line, L, is parallel to BC and passes through A.
Find the equation of L.
Give your answer in the form ax + by + d = 0, where a, b and d are integers.
4a. [2 marks]
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The coordinates of point A are and the coordinates of point B are . Point M is the
midpoint of AB.
Find the coordinates of M.
4b. [2 marks]
is the line through A and B.
Find the gradient of .
4c. [1 mark]
The line is perpendicular to and passes through M.
Write down the gradient of .
4d. [1 mark]
Write down, in the form , the equation of .
5a. [2 marks]
The diagram shows the straight line , which intersects the -axis at and the -axis at
.
Write down the coordinates of M, the midpoint of line segment AB.
5b. [2 marks]
Calculate the gradient of .
5c. [2 marks]
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The line is parallel to and passes through the point .
Find the equation of . Give your answer in the form .
6a. [4 marks]
A right pyramid has apex and rectangular base , with , and
. The vertical height of the pyramid is .
Calculate .
6b. [2 marks]
Calculate the volume of the pyramid.
7a. [3 marks]
The distance from a point to the point is given by
Find the distance from to . Give your answer correct to two decimal places.
7b. [1 mark]
Write down your answer to part (a) correct to three significant figures.
7c. [2 marks]
Write down your answer to part (b) in the form , where and .
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8a. [2 marks]
The equation of the line is .
Write down
(i) the gradient of ;
(ii) the -intercept of .
8b. [2 marks]
The line is parallel to and passes through the point .
Write down the equation of .
8c. [2 marks]
The line is parallel to and passes through the point .
Find the -coordinate of the point where crosses the -axis.
9a. [2 marks]
The four points A(−6, −11) , B(−2, 7) , C(4, 9) and D(6, 3) define the vertices of a kite.
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Calculate the distance between points and .
9b. [4 marks]
The distance between points and is .
Calculate the area of the kite .
10a. [1 mark]
The diagram shows the points M(a, 18) and B(24, 10) . The straight line BM intersects the y-axis at A(0,
26). M is the midpoint of the line segment AB.
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Write down the value of .
10b. [2 marks]
Find the gradient of the line AB.
10c. [3 marks]
Decide whether triangle OAM is a right-angled triangle. Justify your answer.
11a. [1 mark]
The straight line, L1, has equation . The point A has coordinates (6, 0).
Give a reason why L1 does not pass through A.
11b. [2 marks]
Find the gradient of L1.
11c. [1 mark]
L2 is a line perpendicular to L1. The equation of L2 is .
Write down the value of m.
11d. [2 marks]
L2 does pass through A.
Find the value of c.
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12a. [1 mark]
The equation of a line L1 is .
Write down the gradient of the line L1.
12b. [1 mark]
A second line L2 is perpendicular to L1.
Write down the gradient of L2.
12c. [2 marks]
The point (5, 3) is on L2.
Determine the equation of L2.
12d. [2 marks]
Lines L1 and L2 intersect at point P.
Using your graphic display calculator or otherwise, find the coordinates of P.
13a. [4 marks]
The coordinates of point A are (−4, p) and the coordinates of point B are (2, −3) .
The mid-point of the line segment AB, has coordinates (q, 1) .
Find the value of
(i) q ;
(ii) p .
13b. [2 marks]
Calculate the distance AB.
14a. [1 mark]
Line L is given by the equation 3y + 2x = 9 and point P has coordinates (6 , –5).
Explain why point P is not on the line L.
14b. [2 marks]
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Find the gradient of line L.
14c. [3 marks]
(i) Write down the gradient of a line perpendicular to line L.
(ii) Find the equation of the line perpendicular to L and passing through point P.
15a. [2 marks]
The diagram shows points A(2, 8), B(14, 4) and C(4, 2). M is the midpoint of AC.
Write down the coordinates of M.
15b. [2 marks]
Calculate the gradient of the line AB.
15c. [2 marks]
Find the equation of the line parallel to AB that passes through M.
16a. [3 marks]
The diagram shows the straight lines and . The equation of is .
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Find
(i) the gradient of ;
(ii) the equation of .
16b. [2 marks]
Find the area of the shaded triangle.
17a. [2 marks]
The straight line passes through the points and .
Calculate the gradient of .
17b. [2 marks]
Find the equation of .
17c. [2 marks]
The line also passes through the point . Find the value of .
18a. [2 marks]
A line joins the points A(2, 1) and B(4, 5).
Find the gradient of the line AB.
18b. [1 mark]
Let M be the midpoint of the line segment AB.
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Write down the coordinates of M.
18c. [3 marks]
Let M be the midpoint of the line segment AB.
Find the equation of the line perpendicular to AB and passing through M.
19a. [2 marks]
The coordinates of the vertices of a triangle ABC are A (4, 3), B (7, –3) and C (0.5, p).
Calculate the gradient of the line AB.
19b. [1 mark]
Given that the line AC is perpendicular to the line AB
write down the gradient of the line AC.
19c. [3 marks]
Given that the line AC is perpendicular to the line AB
find the value of p.
20a. [2 marks]
The mid-point, M, of the line joining A(s , 8) to B(−2, t) has coordinates M(2, 3).
Calculate the values of s and t.
20b. [4 marks]
Find the equation of the straight line perpendicular to AB, passing through the point M.
21a. [4 marks]
P (4, 1) and Q (0, –5) are points on the coordinate plane.
Determine the
(i) coordinates of M, the midpoint of P and Q.
(ii) gradient of the line drawn through P and Q.
(iii) gradient of the line drawn through M, perpendicular to PQ.
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21b. [2 marks]
The perpendicular line drawn through M meets the y-axis at R (0, k).
Find k.
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