3. The vertices of a triangle are A(1, -2), B(4, 4) and C(-3, 0). (a) Find the distance between A and B. (b) Find the gradient of the line through A and B. (c) Find the equation of the line passing through point C and perpendicular to the line through AB. (d) Prove that triangle ABC is a right-angled triangle.

Q: The distance from the origin to the line passing through the points (0, 1,3) and (1,-1,2) is 14.

A:

Q: ). makes equal intercepts on the axes and passes through the point (2,3). 5. passes through the…

A: (a) Let the equation of the line bexa+yb=1Since it makes equal intercepts on the coordinates axes,we…

Q: a) What is the equation of a straight line that passes through (2,0) and has a gradient of -3 ? b)…

A: a) The given data is: x1,y1=2,0m=-3 To find the equation of the straight line.

Q: 1.) Find the slope and angle of the line joining (2, 2) and (22) that the three points (x,-3), (9,…

A:

Q: Q2) Find the slope of the straight line L1 that passes through the points P1 (0, 6) and P2 (5, 2),…

A: In the given question we have to find the slope of two lines and also tell about that are they…

Q: • Create a symmetric equation of a line with the digits 6, 8 and 4. Does the point D (7,-1,8) lie on…

A:

Q: #3 Find the line equation(s) of the line(s) through point P(1, 0, 1) that meets the following line…

A: Given :  Given:P(1,0,1)L: x,y,x=1,2,0+t2,-1,2P0=1,2,0Aim: To find a line(s) through point P,…

Q: Find the slope of the line containing the points a) (a, 0) and (0, a). b) (a, 0) and (0, b).

A: Given, a) (a,0)and 0,a we know the formula for the slope of the line containing two points is,…

Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

A:

Q: 1) For three 2D points A (x1, y1), B (x2, y2) and C (x3, y3), how would you order these points…

A: Given: Three 2D points A(-1,0), B(-2,0) & C(0,0) We have to order these points counterclockwise.…

Q: 3) The straight line l passes through the points (0,1,5) and (2, –2, 1). Find the y - and z…

A: Using Cartesian equation.

Q: In the following diagram, ABCD form a trapezium. Given that coordinates of E is (0, 4) and…

A:

Q: The perpendicular distance from (5,3) to the line y+4x= 6

A: Line = y+4x-6 = 0 and point ( 5,3)We Know that the perpendicular distance d= ax + by +ca2+b2Where a…

Q: ind the equation of the straight line that 1). makes equal intercepts on the axes and passes through…

A: (1) Let the equation of the line bexa+yb=1Since it makes equal intercepts on the coordinates axes,we…

Q: Which values for x and y make lines r, s, and t parallel? Express your answers as decimals rounded…

A:

Q: Q.I: (a) Find the equation of line that make angle 60° with y-axis and passes through (2, -1). (b)…

A: To solve a) equation of line.  b)to find intercepts.  c) Distance

Q: Q2) Find the slope of the straight line L1 that passes through the points Pl (0, 6) and P2 (5, 2),…

A: Consider the given point for line L1. P1=0,6P2=5,2 Now, find the slope from the above points.…

Q: Prove that the equation of a line passing through (a, 0) and (0, b) (a + 0, b = 0) can be written in…

A: Given points:   (a, 0)  and  (0, b). To prove:  the equation of line passing through these points is…