If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the equation of the line through (x1, yı) and (x2, y2). Use this result to develop a test for collinearity of three yı 1 points.

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A: This is question of 3d geometry and locus.

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A: In the question it is asked to show the reflection of the triangle shown in figure. It is asked to…

Q: Consider the line 15x+16y=16 what is the y-intercept of the parallel line through (16,16).

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Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z 3 -12…

A: The point of intersection will satisfy the line as well as the Planes equation.

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Q: Find the cosine of the angle between the planes -3x - 4y – 3z = 3 and the plane - 1x - 3y + 3z = -2.

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Q: Give a parametric representation for the straight line segment from the point (1,-1,2) to the point…

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Q: Determine the scaler equation of the plane with × -intercept=2, y intercept=-1 and z intercept=3

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Q: calculate the distance between the point P (2, 3) and the point Q (1,-2) 20 3 us O V25 4 jus O V26

A: The distance between two points (x1, y1) and (x2, y2) is                    d=(x2-x1)2+(y2-y1)2…

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

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Q: The plane that passes through the point (5,2,2) and is perpendicular to both x-5z=-24x-5z=-24 and…

A: The direction ratio of the normal vector to the plane x-5z=-24 or x+0y-5z=-24 is (1,0,-5) The…

Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: Describe the plane x = 4.

A: Given, plane x=4we have to describe the plane x=4

Q: Find equations of a line perpendicular to the lines x = y = z and x = 2y = 3z, passing through the…

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Q: The length of the line segment joining the two points of intersection is 3 – x = y = 7+1 With the…

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Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the…

A: consider the direction ratio of line  contaning the point ( 1, 2 ,1 )  is  l , m, n