Answer:
Explanation:
To classify the quadrilateral formed by the given points, we need to find the length of each side and the measure of each angle.
Using the distance formula, we can find the length of each side:
AB = sqrt((4 - (-3))^2 + (2 - 1)^2) = sqrt(49 + 1) = sqrt(50)
BC = sqrt((9 - 4)^2 + (-3 - 2)^2) = sqrt(25 + 25) = 5sqrt(2)
CD = sqrt((2 - 9)^2 + (-4 - (-3))^2) = sqrt(49 + 1) = sqrt(50)
DA = sqrt((-3 - 2)^2 + (1 - (-4))^2) = sqrt(25 + 25) = 5
Using the slope formula, we can find the measure of each angle:
Angle ABC: m1 = (2 - 1)/(4 - (-3)) = 1/7
m2 = (-3 - 2)/(9 - 4) = -1/5
tan(ABC) = |(m2 - m1)/(1 + m1m2)| = 3/4
ABC = arctan(3/4) ≈ 36.87°
Angle BCD: m1 = (-3 - 2)/(9 - 4) = -1/5
m2 = (-4 - (-3))/(2 - 9) = 1/7
tan(BCD) = |(m2 - m1)/(1 + m1m2)| = 3/4
BCD = arctan(3/4) ≈ 36.87°
Angle CDA: m1 = (-4 - 1)/(2 - (-3)) = -1
m2 = (1 - (-3))/(-3 - 9) = 1/2
tan(CDA) = |(m2 - m1)/(1 + m1m2)| = 7/5
CDA = arctan(7/5) ≈ 54.46°
Angle DAB: m1 = (1 - (-4))/(4 - (-3)) = 5/7
m2 = (-4 - (-3))/(-3 - 2) = 1/5
tan(DAB) = |(m2 - m1)/(1 + m1m2)| = 3/4
DAB = arctan(3/4) ≈ 36.87°
Therefore, the quadrilateral formed by the given points is a kite, because adjacent sides are congruent and one diagonal bisects the other diagonal at a right angle.