If A (1, -1),B (0, 4),C (-5, 3) are vertices of a triangle then find the slope of each side.
A (1, -1),B (0, 4),C (-5, 3) are the given points.Slope of line AB = (y2-y1)/ (x2-x1)= (4-(-1))/(0-1)= 5/-1 = -5Slope of line BC = (y2-y1)/ (x2-x1)= (3-4)/(-5-0)= -1/-5 = 1/5Slope of line AC = (y2-y1)/ (x2-x1)= (3-(-1))/(-5-1)= 4/-6 = -2/3Hence the slopes of the sides AB, BC and AC are -5, 1/5 , -2/3 […]
Determine whether the following points are collinear.
(1) A(-1, -1), B(0, 1), C(1, 3) are the given points.Slope of line AB = (y2-y1)/ (x2-x1)= (1-(-1))/(0-(-1))= 2/1 = 2Slope of line BC = (y2-y1)/ (x2-x1)= (3-1)/(1-0)= 2Slope of line AB and BC are equal.Point B lies on both lines.Point A,B,C are collinear. (2) D(-2, -3), E(1, 0), F(2, 1) are the given points.Slope […]
Find the slopes of the lines passing through the given points.
(1) Given A(2,3) and B(4,7)x1 = 2y1 = 3×2 = 4y2 = 7Slope of the line AB = (y2-y1)/ (x2-x1)= (7-3)/(4-2)= 4/2 = 2Hence Slope of line AB is 2. (2) Given P(-3,1) and Q(5,-2)x1 = -3y1 = 1×2 = 5y2 = -2Slope of the line PQ = (y2-y1)/ (x2-x1)= (-2-1)/(5-(-3))= -3/8Hence Slope of line PQ is -3/8. (3) Given C(5,-2) and D(7,3)x1 = […]
Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines.
(1) Given angle made by line with positive direction of X axis, = 45˚.Slope of the line ,m = tanm = tan 45˚ = 1Hence slope of the line is 1. (2) Given angle made by line with positive direction of X axis, = 60˚.Slope of the line ,m = tanm = tan 60˚ = […]