Example 3: Points A, B and C are collinear such that AB:BC = 3:4. Point A is located at (-8, -1) and point C is located at (6, -8). Find the x coordinate of B. To find the coordinates of the partition point (Xp, Yp), of a directed line segment from endpoints (X1, Y1) to (x2, V2) given the ratio a:b Xp %3D Use the following formulas. bx1 + ax2 Xp a + b Xp = by1 + ay2 Yp = Your Turn! Use the same numbers as example 3. Find the y coordinate of B. You only need to show your answer. Yp = a + b

Q: 6. Points U, V, and W are collinear such that 3. If a directed line segment 8. UV: UW : begins at…

A: To find the coordinates of point V.

Q: Evaluate the line integral along the given path(s).

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Find the plane z = a + bx + cy that best fits the data points (0, -4, 0), (5, 0, 0), (4, –1, 1), (1,…

A:

Q: 10. Find the coordinates of point P along the directed line segment AB. A(2, 0), B(12, -5) so that…

A: Here we have, point A(2,0) and point B(12,-5).AP:PB=3:2We have to find coordinate of point P.

Q: Find the directed distance from the given line to the given point. (-1, 6) (5, 4) (10, 8) (1, 2)…

A:

Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the…

A:

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: 6. Given a rule x² + y² = 9, its image rule x? + y² – 2x + 6y +1 = 0 under a translation, state a…

A: To solve the given translation problem.

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: 2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi-…

A: We have to the value of integral.

Q: Find the plane z = a + bx + cy that best fits the data points (0, –4, 0), (5,0, 0), (4, –1, 1), (1,…

A:

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x - 3y + z = -6.

A:

Q: Find the condition for the points (a,0),(h,k),(0,b) when ais not equals to 0 to be collinear

A:

Q: LM is the directed line segment from L(-4,1) to M(5-,5). What are the coordinates of the point that…

A:

Q: A. Use the figure on the right to name each of the following: 1. three collinear points 2. three…

A: A) 1) Collinear points are the points which are on the same line. Hence 3 collinear points are A , P…

Q: The figure shows line AC and line PQ intersecting at point B. Lines A'C' and P'Q' will be the images…

A: Given,

Q: Consider a circle C in the xy-plane. If it is given that the points (2, 3),(2, −1) and (0, 3) are on…

A: Given points are (2, 3),(2, −1) and (0, 3)

Q: Find the work done by the Öeld F = yzi + (xz + 3)j + xyk along the line joining the point A(1, 2, 0)…

A: Given field is,  F = yz i^ + xz+3 j^ + xy k^   The given points is A(1, 2, 0) and B(2, 0, 3). So,…

Q: Let R be the interior of the parallelogram with vertices (-3, 1), (-1,0), (–1,2), and (1, 1).…

A:

Q: 11. Given the coordinates X(0,0), Y(6,3) 0/4 and Z(2,1), find the ratio where point Z partitions the…

A: Use Section formula to solve this question. According to section formula: let coordinates of X is…

Q: 5. Points P, Q, and R are collinear such that PQ: PR If a directed line segment begins at P(2,-4)…

A:

Q: Points F, G, and H are collinear such that FG: FH ==. If a directed line segment begins at F(-5,-1)…

A: Given,  A directed line segment begins at F-5, -1 and ends at H4, -1.  FGFH= 13  We have to find the…

Q: (b) Let A(4,4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

A: Introduction: When a vector is a non-zero scalar multiple of another vector, the two vectors are…

Q: 2. Find the area of a parallelogram defined by PQ and QR when P = (4, 0, 1), Q = (5, -3, 0), and R =…

A:

Q: 2. Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2).

A:

Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

A:

Q: prove Theorem 4P.1 Theorem 4P.1 There are exactly six lines in the four-point geometry.

A: The known fact is that in four point geometry, any two distinct points have exactly one line on both…

Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

A:

Q: Given the points F(8,4) and G(-7,-6) what are the coordinates of the point that partitions the…

A:

Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

A: We will solve the problem

Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: Find the coordinates of point P along the directed line segment AB so that the ratio of AP to PB is…

A:

Q: The vertices of a AABC are A (2, 0, 2), B (- 1, 1, 1) and C(1,-2,4). The points D and E divide the…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

A: The given problem can be proved both by mathematically and by the definition. For your convenience I…

Q: 3. Consider the graph of z=r -y". (a) What shape are the traces parallel to the ry-plane? Are there…

A: given z=x2-y2 (A) what shape are the traces parallel to xy plane? are there any restricition on the…

Q: Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2)

A: Given that: Line is: y=5x+7and collineation is: (x, y)=(2y-x, x-2)

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

A:

Q: Hw-2 If A(X, -2,0),B(-lel,=3)_, C(-4,ile2)_and D(3,0,0)are-points-in Slace thenfind value that…

A:

Q: B) The line passes through the point (2,4,5) and perpendicular to the plane 2x+y- intersects the x-y…

A: Given that the line passes through the point (2, 4, 5) and perpendicular to the plane 2x+y-5z =21

Q: Given four points A(2, 3, 5), B(6,9, 15), C(0,0, 5), D(-2, –3, 10) in 3D Cartesian coordinates, we…

A: We are given four points on the 3D Cartesian coordinates with the image plane as z=2 And we have to…

Q: What are the coordinates of the point on the directed line segment from (-7, 10) to (-2, -5) that…

A: Given points is : -7,10 and -2,-5 m:n=2:3, thereforem=2n=3 -7,10x1=-7y1=10-2,-5x2=-2y2=-5

Q: Find the coordinates of the point Y that lies 2. along the directed line segment from X(-1,3) to…

A:

Q: The diagram shows AB graphed on a coordinate plane. B (4, 6) 6- -5 4 3 2 -5 -4 -3 -2 -1 4 -1- -2 3…

A:

Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

A:

Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

A:

Q: Prove that three points (x1, yl), (x2, y2) and (x3, y3) are collinear ( on the same straight line)…

A:

Q: Points A, B and C are collinear, and AB: BC =1:4. A is located at (-5, - 3), B is located at (-2, 0)…

A: Points A, B and C are colinear . According to the situation we have diagram

Q: hat are the coordinates of the point on the directed line segment from (–7,5) t ',-9) that…

A: In the question we need to find the coordinates of a point which divides the line segment joining…