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.

Q: If A ABC is reflected across the line y-z+ 1, what are the coordinates of Point A post-reflection?…

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

Q: Line segment t and line segment r are parallel. Both line segments are reflected across the y-axis…

A: We have to find the distance between line segments t' and r'

Q: Q5) Find the coefficients a, b, c and d such that the curve defined by; y = ax³ + bx² + cx + d,…

A: Given: The curve y=ax3+bx2+cx+d passes through the points 0, 10, 1, 7, 3, -11, 4, -14. To find: The…

Q: A line 4x + y = 1 through the point A(2, −7) meets the line BC whose equation is 3x - 4y + 1 = 0 at…

A: Let the equation of BC be 3x-4y+1=0      ....(1) and the equation of AB be 4x+y-1=0         ....(2)…

Q: Find the distance between two planes if they are parallel x+2y+3z=6 and 2x+4y+6z=5

A: Solution:GIvenx+2y+3z=6  and 2x+4y+6z=5To find the distanceFormula:If θ=0°  then the planes are…

Q: find the y-intercept of the line that passes through (1,2,-3) and is parallel to the wing 1/3(x-4)=…

A:

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.

Q: Find the coordinates of the point p on the plane #₁ - 2 + 2x3 = 0, that is closest to the point b =…

A: x1-x2+2x3=0  that is closest to the point (2,0,-2)

Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

A:

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x 2s + 2, y = s + 3, z…

A: we have to find the point of intersection of the given lines

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

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

A:

Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

A:

Q: Find the intersection of the line and plane: 3z (2x + y) = -5, P = ( r(t) = (3,-1,0) + t (-3, -2,…

A: Given line : r(t)= (3,-1,0)+t(-3,-2,-1) Given plane : 3z-(2x+y)=-5                       2x+y-3z-5=0…