ABCD is a rhombus. The coordinates of A are (5, 11) The equation of the diagonal DB is y = 3x + 5 The equation of the diagonal AC can be written in the form y = mx + Ċ where m and c are integers. Work out the value of m and the value of c.

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akposevictor akposevictor · Answer 1 · 2022-06-01T10:52:15+02:00

Applying the definition of the diagonals of a rhombus, the value of m is -3, and the value of c is 26.

The diagonals of a rhombus are perpendicular to each other and therefore have slopes that are negative reciprocals.

Equation of diagonal DB is, y = 1/3x + 5.

Slope (m) of DB is 1/3.

Therefore, the slope (m) of diagonal AC would be, -3.

To find the equation of diagonal AC, substitute m = -3 and (5, 11) = (a, b) into y - b = m(x - a)

y - 11 = -3(x - 5)

y - 11 = -3x + 15

y = -3x + 15 + 11

y = -3x + 26

m = -3; c = 26

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