Geometry...Use Slopes & Distance Formula?

Question

Use slopes and the distance formula to show that the quadrilateral whose vertices are (0, 0), (1, 3), (4, 2) and (3, -1) is a square.

Answer 1

Slope:
opposite sides:
(y2 - y2)/(x2 - x1) = (0 - 3)/(0 - 1) = (2 - (-1))/ (4 - 3) = 3
Other pair of opposite sides:
(y2 - y2)/(x2 - x1) =(3 - 2)/(0 - 3) = (0 - (-1))/(0 - 3) = -1/3
Notice also that they are negative reciprocals of each other.
Distance [length of sides] :
D = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(0 - 1)^2 + (0 - 3)^2]
= √[(1 - 4)^2 + (3 - 2)^2]
= √[(4 - 3)^2 + (2 - (-1))^2]
= √[(3 -0)^2 + (-1 - 0)^2] = √10 [All 4 sides equal length]

Answer 2

a million.y=2/3x-7 = (2x-21)/3 3y=2x-21 2x-3y-21=0 slope of line = 2/3 slope of line perpendicular to it = -3/2 answer 2. If there are 2 factors (x,y) and (a,b) the gap between both =the muse of (x-a)(x-a) - (y-b)(y-b) it is the gap formula