Write down the coordinates of point A
Worked Solution & Answer
1 across, 3 up = (1, 3) B1
Answer: (1, 3)
Coordinates — Notes & Worked Examples Show / Hide
Explanation:
Coordinates are always written as (x, y) — go along the corridor (x-axis, horizontal) first, then up or down the stairs (y-axis, vertical). In all four quadrants, left of the origin (0, 0) gives a negative x-coordinate and below the origin gives a negative y-coordinate.
To find the midpoint of a line segment joining (x1, y1) and (x2, y2), average the x-coordinates and average the y-coordinates: Midpoint = (x1 + x22, y1 + y22).
Example 1: A(−3, 2), B(3, 2) and C(3, −2) are three corners of rectangle ABCD. Find the coordinates of D.
D lines up vertically with A (x = −3) and horizontally with C (y = −2). Answer: (−3, −2)
Example 2: Find the coordinates of the midpoint M of the line joining P(−4, 7) and Q(6, −1).
Solution:
Average the x-coordinates and the y-coordinates:
• xM = −4 + 62 = 22 = 1
• yM = 7 + (−1)2 = 62 = 3
Answer: (1, 3)
Plot the point (2, 1) on the grid
Worked Solution & Answer
2 across, 1 up B1
Answer: Point plotted at (2, 1)
Point A is shown on this grid.
(a) Write down the coordinates of point A. [1 mark]
(b) Plot point B on the grid at (2, -2). [1 mark]
Worked Solution & Answer
(a)
Point A is 4 units left of the y-axis and 3 units above the x-axis: (−4, 3). B1
Answer (a): (-4, 3)
(b)
Plot point B 2 units right of the y-axis and 2 units below the x-axis. B1
Answer (b): Point B plotted at (2, -2)
Point A is shown on this grid.
(a) Write down the coordinates of point A. [1 mark]
(b) Plot point B on the grid at (3, -3). [1 mark]
Worked Solution & Answer
(a)
Point A lies on the x-axis at x = 4, y = 0 ⇒ (4, 0). B1
Answer (a): 4, 0
(b)
Go 3 units right and 3 units down from the origin to plot (3, −3). B1
Answer (b): Point B plotted at (3, −3)
The diagram shows a square drawn on a 1-cm square grid.
(a) Write down the coordinates of point A. [1 mark]
(b) Find the perimeter of the square. [1 mark]
cm
Worked Solution & Answer
(a)
Point A is 2 units left and 1 unit up from the origin ⇒ (−2, 1). B1
Answer (a): (-2, 1)
(b)
Each side is 3 cm ⇒ 4 × 3 = 12 cm. B1
Answer (b): 12 cm
(a) Write down the coordinates of point A. (1) (b) Write down the coordinates of point B. (1) (c) Mark and label point C at (–2, 1). (1)
(a) Write down the coordinates of the point A. [1 mark]
(b) Write down the coordinates of the point B. [1 mark]
(c) On the grid, mark with a cross (×) the point (-2, 1)
Label this point C. [1 mark]
Label this point C. [1 mark]
Worked Solution & Answer
(a)
A is at (2, 3) B1
Answer (a): (2, 3)
(b)
B is on the y-axis at (0, –1) B1
Answer (b): (0, –1)
(c)
C plotted at (–2, 1) B1
Answer (c): Point C marked at (–2, 1)
This grid shows a vertical line going through the point P.
(a) Write down the coordinates of point P. [1 mark]
(b) Plot the point (4, -1). [1 mark]
(b) Write down the equation of the vertical line going through point P. [1 mark]
x =
Worked Solution & Answer
(a)
Point P is at x = −2, y = −3 ⇒ (−2, −3). B1
Answer (a): -2, -3
(b)
Plot cross at x = 4, y = −1 on the grid. B1
Answer (b): Point plotted at (4, −1)
(b)
Every point on the vertical line through P has x-coordinate −2 ⇒ x = −2. B1
Answer (b): x = x = -2
The diagram shows points A, B and C on a square grid.
(a) Write down the coordinates of C. [1 mark]
(b) Measure the length of BC.
Give your answer in centimetres. [1 mark]
Give your answer in centimetres. [1 mark]
cm
(c) On the grid, mark with a cross (×) the point D so that ABCD is a parallelogram.
Label this point D. [1 mark]
Label this point D. [1 mark]
Worked Solution & Answer
(a)
(2, –1) B1
Answer (a): 2, –1
(b)
√(2² + 3²) = √13 ≈ 3.6 cm B1
Answer (b): 3.6 cm
(c)
D = (2 – 3, –1) = (–1, –1) B1
Answer (c): D marked at (–1, –1)
Work out
(a) Coordinates of C (1) (b) Mark point D so ABCD is a square (1) (c) Midpoint of BC (1)
(a) Coordinates of C (1) (b) Mark point D so ABCD is a square (1) (c) Midpoint of BC (1)
(a) Write down the coordinates of point C. [1 mark]
(b) On the grid, mark with a cross (×) the point D so that ABCD is a square. [1 mark]
(c) Write down the coordinates of the midpoint of the line segment BC. [1 mark]
Worked Solution & Answer
(a)
(0, –1)
Answer (a): (0, –1)
(b)
Vector BA = (3, 1), so CD = (3, 1) ⇒ D = (0 + 3, –1 + 1) = (3, 0) B1
Answer (b): Cross marked at (3, 0)
(c)
Midpoint of (–1, 2) and (0, –1) = ((–1+0)/2, (2–1)/2) = (–0.5, 0.5) B1
Answer (c): (–0.5, 0.5)
Triangle ABC is drawn on the grid.
(a) Write down the coordinates of the point B. [1 mark]
(b) On the grid, plot the point D(4, -1). Label it D. [1 mark]
(c) Write down the special name for triangle ABC. [1 mark]
(d) Find the coordinates of the midpoint of AC. [2 marks]
Worked Solution & Answer
(a)
(6, 2)
Answer (a): (6, 2)
(b)
D plotted at (4, −1)
Answer (b): D plotted at (4, −1)
(c)
Isosceles
Answer (c): Isosceles
(d)
((2 + 4)/2, (2 + 7)/2) = (3, 4.5) M1 A1
Answer (d): (3, 4.5)