To classify a quadrilateral by its sides, we need to calculate the distance between each pair of its vertices.
The distance between Q and R is the square root of ((1-(-2))^2 + (5-(-1))^2) = square root of (3^2 + 6^2) = square root of (9+36) = square root of 45 = 6.7
The distance between R and T is the square root of ((-8-1)^2 + (-4-5)^2) = square root of (9+81) = square root of 90 = 9.5
The distance between Q and T is the square root of ((-8+2)^2 + (-4+1)^2) = square root of (10+5) = square root of 15 = 3.87
If the quadrilateral is a rectangle, two sides of it have to be equal, so in this case, AQRT is not a rectangle.
If the quadrilateral is a rhombus, all four sides have to be equal, so in this case, AQRT is not a rhombus.
If the quadrilateral is a square, all four sides have to be equal, so in this case, AQRT is not a square.
If the quadrilateral is a trapezoid, two adjacent sides are parallel, so in this case, AQRT is not a trapezoid.
If the quadrilateral is a parallelogram, two pairs of opposite sides are parallel, so in this case, AQRT is not a parallelogram.
If the quadrilateral is a kite, two pairs of sides have the same length, so in this case, AQRT is not a kite.
So the only possible classification is that AQRT is a general quadrilateral.
so we have:
QR = 6.7
RT = 9.5
QT = 3.87