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Point A is plotted at (4, -2) on this one-centimetre square grid - OCR - GCSE Maths - Question 7 - 2020 - Paper 3

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Point A is plotted at (4, -2) on this one-centimetre square grid. Point A is a corner of a square with area 36 cm². The other corners of the square have integer coo... show full transcript

Worked Solution & Example Answer:Point A is plotted at (4, -2) on this one-centimetre square grid - OCR - GCSE Maths - Question 7 - 2020 - Paper 3

Step 1

Determine the side length of the square

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Answer

To find the side length of a square with an area of 36 cm², we can use the formula for area: A=s2A = s^2 where ss is the side length. Thus: s=36=6 cms = \sqrt{36} = 6 \text{ cm}

Step 2

Identify points using grid system

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Answer

Since point A is at (4, -2), the diagonally opposite corner of the square will be opposite at a distance of the side length in both x and y directions.

The movement will be as follows:

  • Move 6 cm to the right (adding 6 to the x-coordinate): 4+6=104 + 6 = 10
  • Move 6 cm upwards (adding 6 to the y-coordinate): 2+6=4-2 + 6 = 4

Thus, one possible coordinate for the opposite corner of the square is (10, 4).

Furthermore, the other possible coordinate can be obtained by moving left and downward:

  • Move 6 cm to the left (subtracting 6 from the x-coordinate): 46=24 - 6 = -2
  • Move 6 cm downward (subtracting 6 from the y-coordinate): 26=8-2 - 6 = -8

This gives a second possible coordinate of (-2, -8).

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