Question

Quadrilateral ABCD with vertices A(4, 3), B(4, -2), C(-4, -2) and D(-4, 3) is a rectangle, find the length of the diagonals.

Answer 1

Distance between two points P(x1,y1), Q(x2,y2):
D=sqrt((x2-x1)^2+(y2-y1)^2)

Polygons are generally named in order along the perimeter, so that for a rectangle ABCD, AC or BD are diagonals.
Here, we need the distance between points A(4,3) and C(-4,-2)
Applying the above formula for distance between two points,

D=sqrt((4-(-4))^2+(3-(-2))^2)=sqrt(8^2+5^2)=sqrt(64+25)=sqrt(89)