Question

rhombus CDEF is shown below. If the slope of FC is 25, what must be the slope of CD in order for CDEF to be a square?

Answer 1

`-(1)/(25)`

Explanation:

Given the rhombus CDEF, sides FC and CD are adjacent sides.

Using coordinate geometry, to proof that a quadrilateral is a square, with regards to the slope, the slope of adjacent segments must be negative reciprocals.

In fact, by definition: Two lines with slopes
`m_1$ and m_2` are perpendicular if:

`m_1=-(1)/(m_2)`

Therefore if :

• FC and CD are adjacent segments
• Slope of FC=25

For the rhombus to be a square:

Slope of CD
`=-(1)/(25)`