O Level & IGCSE · Maths 0580 · Coordinate Geometry & Graphs
Coordinate Geometry — Worksheet
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Full text of Coordinate Geometry — Worksheet
1 P is the point (
- , 1) and Q is the point (6, 13). M is the midpoint of the line PQ.
- Find the coordinates of M.
( ...................... , ...................... ) [1]
- (i) Find the gradient of the line PQ.
................................................. [2]
- Write down the gradient of a line that is perpendicular to the line PQ.
................................................. [1]
Coordinate Geometry Worksheet
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Section:
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2 D is the point (4, 6) and E is the point (e, e).
- The length of DE is 20.
Form an equation in e and solve it to find the possible coordinates of E. Show your working.
(............... , ...............) or (............... , ...............) [5]
- F is the point ( ,f
- f5 ).
The gradient of the perpendicular bisector of DF is 2
3.
- Find the value of f.
f = ................................................. [4]
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- The equation of the perpendicular bisector of DF is y x k = + .
Find the value of k.
k = ................................................. [3]
- PQR is an isosceles triangle with PR = QR. P is the point (1, 5) and Q is the point (5, 1). Angle PRQ is not a right angle.
Find the coordinates for one possible position of R. You may use the grid to help you.
y x O
( ...................... , ...................... ) [2]
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- A is the point (-1, -5) and B is the point (3, 3).
Find the equation of the line perpendicular to AB which passes through the midpoint of AB.
................................................. [5] 4 P is the point (h, 7). P lies on the line y x + = .
- Find the value of h.
h = ................................................. [2]
- Line L is perpendicular to the line y x + = and passes through P.
Find the equation of line L.
................................................. [4]
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The vertices of a triangle are A (7, 0), B (-1, 6) and C (-1, -4).
- Show that AB = BC.
[3]
- Find the area of triangle ABC.
............................................ unit2 [2]
P is the point (–3, 4), Q is the point (5, 1).
- M is the midpoint of PQ.
Find the coordinates of M.
Answer ( ................. , ................. ) [1]
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- Find the gradient of PQ.
Answer .......................................... [1]
- R is the point (– 6, 0), O is the point (0, 0).
Which of the points, R or P, is closer to O? Show your working.
Answer point ................................. [2]
7 A is the point (–4, –1) , B is the point (2, 2) and BC = - e o .
- Find the coordinates of the midpoint of AB.
Answer ( ................... , ..................) [1]
- Find the gradient of AB.
Answer ........................................... [1]
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- Show that BC is perpendicular to AB.
[2]
8 The coordinates of P and M are (-3, 10) and (0, 4).
- Find the gradient of the line PM.
Answer .......................................... [1]
- Find the equation of the line PM.
Answer .......................................... [1]
- M is the midpoint of PQ.
Find the coordinates of Q.
Answer ( .................. , .................) [2]
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9 A is the point (0, 3), B is the point (1, 5) and C is the point (p, –1).
- Find the equation of the line AB.
Answer ........................................... [2]
- The gradient of the line BC is
- .
Find the value of p.
Answer p = ..................................... [2]
10 The coordinates of the midpoint of the line AB are (1, 2). The length of the line AB is 10 units.
- If the gradient of AB is 0, find the coordinates of A and B.
Answer A = (............ , ............)
B = (............ , ............) [1]
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- If the gradient of AB is 4
3, find the coordinates of A and B.
Answer A = (............ , ............)
B = (............ , ............) [2]
11 P is the point (1, –3) and Q is the point (7, 2).
- Find the coordinates of the midpoint of PQ.
Answer ( .................... , .................... ) [1]
- Find the gradient of the line PQ.
Answer ................................................. [1]
- The line, L, with equation 2x – 5y = k, passes through the point Q.
- Find the value of k.
Answer k = ................................................. [1]
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- The line x + Ay = 3 is parallel to L.
Find the value of A.
Answer A = ................................................. [1] y x
K
J
- Find the gradient of line J.
Answer ............................................ [1]
- Write down the equation of line K.
Answer ............................................ [1]
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(iii) Draw a line, L, through (6, 1) such that the area enclosed between J, K and L is 6 cm2.
[1]
- Find the equation of line L.
Answer ............................................ [2]
- The line N is perpendicular to line J at (2, 2) .
Find the coordinates of the point where line N crosses the y-axis.
Answer ............................................ [2] 13 P is ,4 4 - ^ h and Q is ,3 - ^ h.
M is the midpoint of PQ.
- Find the coordinates of M.
Answer ( ................... , ...................) [1]
- Find the gradient of the line PQ.
Answer ............................................. [1]
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- Q is the midpoint of the line PQR.
- Find the coordinates of R.
Answer ( .................... , ..................) [2]
- Write down the value of MR
PM .
Answer ............................................. [1]
P is (−1, 3) and Q is (5, −1).
- Find the coordinates of the midpoint of PQ.
Answer ( ............... , ..............) [1]
- Find the gradient of the line PQ.
Answer ............................................... [1]
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- Given that the length of PQ = n units, where n is an integer, find the value of n.
Answer n = ........................................ [2]
A line has equation 3y = 2 – x
- Find the gradient of the line
Answer [1]
- The line passes through the point (5, k)
Find the value of k
Answer k = [1]
16 A is the point (0, 4) and B is the point (–6, 1).
- M is the midpoint of the line AB.
Find the coordinates of M.
Answer (............, ............) [1]
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- Find the equation of the line AB.
Answer .....................................[2]
You may use the graph paper on the next page to help answer this question.
The point A is (0, 7), and the point B is (6, 9).
(a) Express →
AB as a column vector.
...................................... [1]
- Find the gradient of AB.
...................................... [1]
- The equation of the line AB is x + Py + Q = 0 .
Find P and Q.
Answer P = ............................... [2]
Q = ............................... [2]
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- The point C is (12, 2).
- Given that C is the midpoint of BM, find the coordinates of M.
Answer (........... , ...........) [1]
- Calculate AC.
Answer .............................. units [1]
The point D lies on the line AB. The line CD is parallel to the y-axis.
Find the coordinates of D.
Answer (........... , ...........) [2]
(iii) (a)
18 P is the point (–2, 1) and Q is the point (3, 7).
- M is the midpoint of PQ.
Find the coordinates of M.
Answer (............, ............) [1]
- Find the gradient of the line PQ.
Answer ........................................ [1]
- The line with equation 2y + 3x + k = 0 passes through the point P.
- Find k.
Answer k = .................................. [2]
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- Find the gradient of this line.
Answer ........................................ [1]
A straight line passes through the points P (–8, 10) and Q (4, 1).
Find
- the coordinates of the midpoint of PQ,
- (............... , ................) [1]
- the equation of PQ.
- ..................................... [2]
