Question

How that the points a(2, -2), b(14, 10), c(11, 13) and d(-1, 1) are the vertices of a rectangle.

Answer 1

a(2, -2)

b(14, 10)

c(11, 13)

d(-1, 1)

now determine side AB BC CD and AD

by using distance formula

AB =√[(x2-x1)^2+(y2-y1)^2]

AB = √[(14-2)^2+(10+2)^2]

AB = √[144+144]

AB = √[288]

AB = 12√2

BC = √[(x3-x2)^2+(y3-y2)^2]

BC = √[(11-14)^2+(13-10)^2]

BC = √[ (-3)^2+(3)^2]

BC = √[9+9]

BC = 3√2

CD = √[(x4-x3)^2+(y4-y3)^2]

CD = √[(-1-11)^2+(1-13)^2]

CD = √[ (-12)^2+(-12)^2]

CD = √[144+144]

CD = √[288]

CD = 12√2

AD = √[(x4-x1)^2+(y4-y1)^2]

AD = √[(-1-2)^2+(1+2)^2]

AD = √[9+9]

AD = 3√2

in rectangle opposite sides are equal

AB = CD = 12√2

BC = AD = 3√2