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

Answer:

$-\dfrac{1}{25}$

Step-by-step 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:

$m_1=-\dfrac{1}{m_2}$

Therefore if :

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

For the rhombus to be a square:

Slope of CD $=-\dfrac{1}{25}$