Question

Please help I am very confused!!!!!!!!!

A square has vertices (1,7), (1,2), (6,7), and (6,2). What is the area of the square? How can you find the area of the square without drawing the square in a coordinate plane? Explain.

Answer 1

25 units²

Explanation:

Area of square = side ²

Area = (6 - 6)² + (7 - 2)²

Area = 5²

Area = 25 units²

Answer 2

(x,y)
x=right left direction
y=up down direction

we see the points (1,7) and (1,2)
they didn't move anywhere to the right or left since the first number didn't change
it went 5 units down though (7 to 2 is 5 units)

then the next one
look at the ones with same numbers in the same place

(1,7) and (6,7)
didn't move up or down but moved 5 units left and right (1 to 6 is 5 units)

(6,7) and (6,2)
didn't move left or right but moved down 5 units (7 to 2 is 5)

(6,2) and (1,2)
didn't go up or down but went 5 units down (6 to 1 is 5)


so we have that the points are 5 away from each other (the ones that are stright up and left or righ tof each other (not diagonal))

therefor the legnth of each side is 5 units

area=5^2=25

anothe way is
square has 4 sides equal
find 1 side and you found other 3
pick 2 points with same first number or second number and find difference

(1,7) to (1,2)
difference of 5 (7 to 2 is 5)

therefor area=5^2



25 square units