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A rhombus is drawn on a coordinate grid - OCR - GCSE Maths - Question 19 - 2023 - Paper 5
Question 19
A rhombus is drawn on a coordinate grid. One diagonal of the rhombus has equation $y = \frac{1}{2}x + 3$. The other diagonal passes through the point (1, 7). Find... show full transcript
Worked Solution & Example Answer:A rhombus is drawn on a coordinate grid - OCR - GCSE Maths - Question 19 - 2023 - Paper 5
Step 1
Find the gradient of the given diagonal
Answer
The equation of the first diagonal is given as (y = \frac{1}{2}x + 3). Therefore, the gradient (m) of the first diagonal is (m = \frac{1}{2}). The gradient of the second diagonal of a rhombus is the negative reciprocal of the first diagonal's gradient. Thus, the gradient (m_2) of the second diagonal is given by:
Step 2
Use the point-slope form to find the equation
Answer
Given that the second diagonal passes through the point (1, 7) and has a gradient of (-2), we can use the point-slope form of the equation:
Substituting (x_1 = 1), (y_1 = 7), and (m = -2), we get:
Expanding this, we find:
Therefore, simplifying gives:
Step 3