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KS3 · Geometry and Measures

KS3.M-G13 Coordinates and Line Geometry

Calculators not allowed · about 60 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Look at the point P( -3, 4 ). State which quadrant P lies in.

(1)

Write down the coordinates of each labelled point.

Figure (to be drawn): A 4-quadrant grid with points A, B, C and D plotted: A at (2, 3), B at (-4, 1), C at (-1, -2), D at (5, -3).

(a)Point A(1)

(b)Point B(1)

(c)Point C(1)

(d)Point D(1)

Reflect the point R(4, -2) in the x-axis. Write down the coordinates of the image.

(1)

Reflect the point S(-5, 6) in the y-axis. Write down the coordinates of the image.

(1)

Find the midpoint of the line joining the points A(2, 5) and B(8, 1).

(2)

Find the midpoint of C(-3, -4) and D(1, 2).

(2)

Calculate the distance between the points that lie on the same horizontal or vertical line.

(a)Distance between E(3, 7) and F(3, -2).(1)

(b)Distance between G(-6, 4) and H(2, 4).(1)

Work out the gradient (slope) of each line joining the two points. Give answers as fractions or integers.

(a)Gradient of line through J(1, 2) and K(4, 11).(2)

(b)Gradient of line through L(-2, 5) and M(4, 2).(2)

A straight line passes through the points P(0, 3) and Q(2, 7). Work out the equation of the line in the form y = mx + c.

(3)

Mark scheme · KS3.M-G13 Coordinates and Line Geometry

Question 1

B1 Second quadrant cao (x negative, y positive)
Answer: Second quadrant

Question 2

(a) B1 (2, 3) cao
(a) Answer: (2, 3)
(b) B1 (-4, 1) cao
(b) Answer: (-4, 1)
(c) B1 (-1, -2) cao
(c) Answer: (-1, -2)
(d) B1 (5, -3) cao
(d) Answer: (5, -3)

Question 3

B1 (4, 2) cao (reflecting in x-axis changes sign of y)
Answer: (4, 2)

Question 4

B1 (5, 6) cao (reflecting in y-axis changes sign of x)
Answer: (5, 6)

Question 5

M1 midpoint method used: ((2+8)/2, (5+1)/2) or equivalent
A1 (5, 3) cao
Answer: (5, 3)

Question 6

M1 midpoint method used: ((-3+1)/2, (-4+2)/2) or equivalent
A1 (-1, -1) cao
Answer: (-1, -1)

Question 7

(a) B1 9 cao (difference in y: 7 - (-2) = 9)
(a) Answer: 9
(b) B1 8 cao (difference in x: 2 - (-6) = 8)
(b) Answer: 8

Question 8

(a) M1 difference method shown: (11 - 2)/(4 - 1) or equivalent
(a) A1 3 cao
(a) Answer: 3
(b) M1 difference method shown: (2 - 5)/(4 - (-2)) or equivalent
(b) A1 -1/2 cao
(b) Answer: -1/2

Question 9

M1 find gradient m = (7 - 3)/(2 - 0) or equivalent
M1 substitute a point to find c, e.g. 3 = m*0 + c or use y = mx + c
A1 y = 2x + 3 cao
Answer: y = 2x + 3

Coordinates and Line Geometry - Worksheets, Questions and Revision