Question

ABCD is a rhombus.

The coordinates of A are (5,11)
The equation of the diagonal DB is y =
`(1)/(3)` 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

m = - 3 and c = 26

Explanation:

• the diagonals of a rhombus are perpendicular bisectors of each other

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y =
`(1)/(3)` x + 5 ← is in slope- intercept form

with slope m =
`(1)/(3)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(3) )` = - 3 , then

y = - 3x + c ← is the partial equation of AC

to find c substitute A (5, 11 ) into the partial equation

11 = - 15 + c ⇒ c = 11 + 15 = 26

y = - 3x + 26 ← equation of diagonal AC

with m = - 3 and c = 26