option c. square

step-by-step explanation:

points to remember

distance formula

length of a line segment with end points (x1, y1) and (x2, y2) is given by,

distance = √[(x2 - x1)² + (y2 - y1)²]

to find the sides of quadrilateral lmno

l (1, 1), m (4, 4), n (7, 1), and o (4, −2)

lm = √[(4 - 1)² + (4 - 1)²]

= √[3² + 3²]

= √(9+ 9) = √18

mn = √[(7 - 4)² + (1 - 4)²]

= √[3² + (-3²)]

= √(9+ 9) = √18

on = √[(4 - 7)² + (-2 - 1)²]

= √[(-3)² + (-3²)]

= √(9+ 9) = √18

lo = √[(4 - 1)² + (-2 - 1)²]

= √[3² + (-3²)]

= √(9+ 9) = √18

to find the type of quadrilateral

here lm = mn = no = lo = √18

all sides are equal.

therefore the correct answer is option c. square

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