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A pattern is made from four congruent right-angled triangles - OCR - GCSE Maths - Question 7 - 2020 - Paper 1
Question 7
A pattern is made from four congruent right-angled triangles. The line AC is parallel to the x-axis. The point A has coordinates (4, 9) and the point B has coordina... show full transcript
Worked Solution & Example Answer:A pattern is made from four congruent right-angled triangles - OCR - GCSE Maths - Question 7 - 2020 - Paper 1
Step 1
Work out the coordinates of point C
Answer
Since line AC is parallel to the x-axis, point C will have the same y-coordinate as point A, which is 9. Thus, the x-coordinate can be determined by analyzing the triangle shape. Given the coordinates of B (17, 12), point C would lie directly below B horizontally, which means its x-coordinate will be the same as that of B. Therefore,
Coordinates of C: (17, 9)
Step 2
Work out the coordinates of point D
Answer
To find point D, we note that it is vertically aligned with point A. Since point A has coordinates (4, 9) and given the triangles are congruent, the x-coordinate of D will remain the same as A (4) but its y-coordinate will be lower than A's. Thus, it will equal the y-coordinate of point C (9) minus the height of the triangle. Assuming the height is equal to the vertical distance from B to C (which is 12 - 9 = 3), the y-coordinate of D will be:
9 - 3 = 6.
Thus, the coordinates of D are:
Coordinates of D: (4, 6)