In the diagram below, L(-5; -2), M(-1; -6) and K(5; 4) are the vertices of AKLM in a Cartesian plane. K( 5: 4) L(-5; -2 )< M(-1: -6 ),

Q: 2. (a) Show that the points (-2x, 5x), (0, 4x), (6x, x) are collinear.

A: Given that: (-2x, 5x), (0, 4x) , (6x, x)

Q: find aplane through Po (2,!,-1) and perpendicular to the line of Intersectionof the planes 2xty-Z=3)

A:

Q: Describe a method for determining whether four points P, Q , R , and S lie in the same plane?

A: We will show a method for determining whether four points P,Q,R and S lie in the same plane.

Q: Show that three points P , Q, R are collinear (lie on a line)if and only if −→P Q × −→P R = 0.

A: Given: Show that three points P, Q, and R are collinear (lie on a line) if and only if PQ→×PR→=0

Q: Which point is one fourth of the way between point A and point B on the line segment AB shown on the…

A: Here we will find the point which is one forth of the way between point A and point B,

Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

A:

Q: Show that the quadrilateral with the given vertices is a parallelogram. E(-5,-2), F(-3,3), G(3,5),…

A:

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

A: Solve the given

Q: The end points of line segment 4, which lies in the xy-plane, are (-2, 5) and (6,-3). Which of the…

A: i have used the formula of midpoint of the two points and the slope point form of the straight line…

Q: 3) Write an equation in point-slope form for the perpendicular bisector of the segment with ndpoints…

A: line passing through point p(6, 3) and Q(2, -3)  To find:- Point - slope form Equation of line which…

Q: Show that (km) is the number of paths in a square grid from (0,0) to the point (m,n) on the diagonal…

A:

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

A: From Geometry: Line can be parallel to plane, intersect the plane or lie in the plane. Only third…

Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 are parrallel.

A:

Q: Find b and c so that y = – 5z² + bz + c has vertex (9, 1). c =

A: The given equation y=-5x2+bx+c has a vertex at (9, 1). The given equation is an equation of a…

Q: Verify that the points are vertices of a parallelogram and find its area A(2,-3,1) B(6,5,-1)…

A:

Q: 4. 3 2. 54 3-2 -1 1 2 4. -2 -3 -4 -5 -61 3.

A:

Q: Suppose that receiving stations X, Y. and Z are located on a coordinate plane at the points (5,10).…

A:

Q: A line passes through the points (12 m, 8 m) and (-3 m, -5 m). Determine the perpendicular distance…

A: Given: Points: (12, 8) and (-3, -5)

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

A:

Q: What are the coordinates of the vertices of AA'B'C' after a reflection across a line through point P…

A: Given, ∆A'B'C' is formed after a reflection across a line through point P followed by a translation…

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: 7. Reflect parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,–4) in the line y = -x.…

A: Reflection in Y axis  : (x , y ) → (-x , - y )

Q: Find b and c so that y=18x2+bx+c has vertex (9,−6)

A:

Q: Find the equation of the perpendicular bisector of th segment joining the points A(2, 3) and…

A:

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: The base of a triangle passes through a fixed point (f,g) and its sides are bisected respectively at…

A: y2-8xy-9x2=0 y2-9xy+xy+9y2=0y(y-9x)+x(y-9x)=0(x+y)(y-9x)=0 here we have two lines  L1:…

Q: a). Determine a pair of planes whose intersection is the given line. = 2-3k, y = 3+e , Z- 2 -4€

A: Note: as per our guidelines we are supposed to answer only one question.* *Kindly repost other…

Q: Which of the points A(-4,0,–1), B(3,1,–5), and C(2,4, 6) is closest to the yz-plan Which point lies…

A: Given: A(-4,0,-1)  B(3,1,-5)  and C(2,4,6) To find: Which is closet to the yz plane Which is lies on…

Q: 7. The diagonals of Parallelogram ABCD intersect at point X, the mAX is 152.

A:

Q: e find aplane through Po (2,,,-1) and Perpendicular to the line of Intersection of the planes…

A: Equation of plane

Q: 2) 2 4-2

A:

Q: Use the result in Exercise 21 to find the equation of the line that contains (4, 5) and is…

A: Given- 2x+3y=6 To find- The equation of the line which is passing through the point 4,5 and…

Q: For Fano's geometry, prove that the lines through any one point of the geometry contain all the…

A: Given detail: For Fano's geometry, prove that the lines through any one point of the geometry…

Q: Find a plane containing the point (-5,7,-6) and the line 7(t) : +t

A:

Q: In the diagram below, draw the two limiting parallel lines to the given line I and a point P on the…

A:

Q: 3. What are the three possibilities for the intersection of a line and a plane?

A: The solution is given in the next step.

Q: 3 -2-1 -2 -3 -4 -5 -6V How can we

A:

Q: If two planes intersect, is it guaranteed that the method of setting one of the variables equal to…

A: Let say one the intersecting two planes is Ax + By + Cz =D When we put z = 0 the Plane reduces to…

Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: Suppose  three points on a plane are defined as A=(8,2) B=(-1,-10) C=(-8,14) all lengths  are in…

A: Here we find the distance between the points and check the formation of the triangle.

Q: Find the angle between the planes (x+y+za1)and. (x-24+32-1). And find the Symmetricequations for the…

A:

Q: If c > 5, how many lines through the point (0, c) are normal 29 lines to the parabola y = x²? What…

A:

Q: Which point is one fourth of the way between point A and point Bon the line segment AB shown on the…

A:

Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = &lt;1, -1,…

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

A:

Q: Fix one vertex at (0,a) in the (x,y)-plane and move another vertex along the x-axis. Show that the…

A: Given: A fixed vertex 0,a A second vertex moving along the x-axis. To show: The locus of the third…

Q: Use the result in Exercise 20 to find the equation of the line that contains (4, 5) and is parallel…

A: We know the important theorem is that the graph of Ax+By=C is parallel to the graph of Ax+By=D.…

Q: AJKL has vertices J(1,-3), K(4, –3), and L(3,1). Reflect AJKL across the y-axis and then rotate it…

A:

Q: Which point is two fifths of the way between point A and point B on the line segment AB shown on the…

A: Given query is to find the point at distance 2/5 from A.