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ABCDA is a rhombus - Edexcel - GCSE Maths - Question 18 - 2017 - Paper 1

Question 18

ABCDA is a rhombus. The coordinates of A are (5, 11) The equation of the diagonal DB is y = -\frac{1}{2}x + 6 Find an equation of the diagonal AC.

Worked Solution & Example Answer:ABCDA is a rhombus - Edexcel - GCSE Maths - Question 18 - 2017 - Paper 1

Step 1

Understanding the relationship between diagonals

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Answer

Since ABCD is a rhombus, the diagonals AC and DB bisect each other at right angles, meaning that the gradient of AC is the negative reciprocal of the gradient of DB. Given the equation of DB is y = -\frac{1}{2}x + 6, the gradient of DB (m_DB) is -\frac{1}{2}, thus:

$m_{AC} = -\frac{1}{m_{DB}} = -\frac{1}{-\frac{1}{2}} = 2$

Step 2

Finding the equation of diagonal AC

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Answer

The gradient of AC has been determined to be 2. We now need a point on line AC. Since point A has coordinates (5, 11), we can use point A to find the equation of AC using the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$ Substituting the values from point A (5, 11):

$y - 11 = 2(x - 5)$ Expanding this gives:

$y - 11 = 2x - 10$ Thus, $y = 2x + 1$ Therefore, the equation of diagonal AC is:

$y = 2x + 1$

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