Figure lmno is located at l (1, 1), m (4, 4), n (7, 1), and o (4, −2). use coordinate geometry to best classify quadrilateral lmno.
a. kite
b. parallelogram
c. square
d. trapezoid

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

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis