3. On area and volume (a) Find the area of the triangle passing through the poin
ID: 3136294 • Letter: 3
Question
3. On area and volume (a) Find the area of the triangle passing through the points (-1, 1),(1,0), (0,3). (b) Find the area of the triangle passing through the points (-1,-1), (1,3), (2,5) (c) Find the area of the triangle passing through the points (1, 1), (2,1),(,-1). (d) Find the area of the triangle passing through the points (1, 1),(2,4), (3,9). Also determine, if the points are collinear. Also determine if the points are collinear. Also determine if the points are collinear. Also determine, if the points are collinear.Explanation / Answer
3. The area of the ABC is given by |[ Ax(By-Cy) +Bx(Cy-Ay)+Cx(Ay-By)]/2| , where Ax and Ay denote the x and y coordinates of the point A. The x and y coordinates of the points B and C are denoted in the same way.
(a). The area of the given is | 1/2[ (-1)(0-3)+1(3-1)+0(1-0)]| = |(1/2)(3+2)]| = 5/2.Hence the given point are not collinear.
(b). The area of the given is | 1/2[(-1)(3-5)+1(5+1)+2(-1-3)]| = |1/2[2+6-8)]| = 0. Hence the given point are collinear.
(c ). The area of the given is | 1/2[1(1+1)+2(-1-1)+(1-1)] = |(1/2) (2-4)]| = 1. Hence the given point are not collinear.
(d). The area of the given is | 1/2[1(4-9)+2(9-1)+3(1-4)]| = |(1/2)(-5+16-9)]| = 1. Hence the given point are not collinear.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.