Photo AI

A pattern is made from four identical rectangles - Edexcel - GCSE Maths - Question 14 - 2021 - Paper 3

Question icon

Question 14

A-pattern-is-made-from-four-identical-rectangles-Edexcel-GCSE Maths-Question 14-2021-Paper 3.png

A pattern is made from four identical rectangles. The sides of the rectangles are parallel to the axes. Point A has coordinates (3, 4) Point B has coordinates (11, ... show full transcript

Worked Solution & Example Answer:A pattern is made from four identical rectangles - Edexcel - GCSE Maths - Question 14 - 2021 - Paper 3

Step 1

Set up equations for the dimensions (width and height)

96%

114 rated

Answer

Let the width of each rectangle be denoted by ( w ) and the height by ( h ). The pattern consists of four rectangles forming a specific height and width:

  1. The coordinates of A are given as (3, 4).
  2. The height from A to B is given by the y-coordinates, thus: [ h = 20 - 4 = 16 ]
  3. The width from A to C could be expressed in terms of the unknown width ( w ): [ w = 11 - 3 = 8 ]

Step 2

Solve for both variables

99%

104 rated

Answer

Using the heights and widths, we can verify:

  1. From A to B: Height ( h = 16 )
  2. From A to C horizontally: Width ( w = 8 ) Thus, we have derived functional relationships: two rectangles stacked and two rectangles in width. We observe: [ 2h = 20, \quad 2w = 8 ] Substituting yields: [ h = 8, \quad w = 4 ]

Step 3

Find the coordinates of C

96%

101 rated

Answer

With A (3, 4), we travel rightwards by the width ( w ) of rectangles:

  1. Starting at A (3, 4), moving horizontally to the right: [ C_x = 3 + 8 = 11 ]
  2. And vertically: [ C_y = 4 + 0 = 4 ] Thus, the coordinates of C are (11, 4).

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;