Question

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

Answer 1

From the information given, it is correct to state that M = - 3; while c = 26. This problem relates to a Rhombus. See the definition of a Rhombus below.

What is a Rhombus?

A Rhombus is a 2-dimensional quadrilateral whose sides have equal length.

What are the steps for finding M and C?

It is given that ABCD is a Rhombus. This means that

• AC ⊥ BD; and
• Line DB is y = (1/3)x + 5

Hence, the slope of AC = -3.

This is arrived at as follows:

Given that the diagonals of Rhombus' are perpendicular, hence

I/3 x m = -1 ⇒ -3

⇒ Line y-11 = -3 (x-5)

⇒ Line AC thus ⇒ y = -3x + 26

How do we solve for c?

Recall that the coordinates are (5, 11). Thus let y = -3x + b

Hence, -3 x 5 + b = 11
b = 11 + 15

b = 26.

Therefore the equation is given as:

y = -3X + 26 were:

m = -3; and

c = 26

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