Exercise 1.5. Consider coordinates in the plane; i.e., pairs (a, b) where a,b e R. Recall that two coordinate pairs (a, b) and (c, d) are comparable if either (a) a

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

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

Q: Use drawings as needed to answer the given question

A: (a) In Euclidean geometry, if two or more than two points lie on a line close to or far from each…

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z ] = [− 1, − 9, 16]+t…

A: The given line is [ x, y , z] = [ -1, -9, 16]  +  t   [ 3, 3, -5]  and the given plane is x+4y+3z=11…

Q: 25. Find the intersection of the line [x, y, z] 2х — 4у + 7z —26 %3D 0. [1,4, – 2] + t[1, – 1,3] and…

A:

Q: Find the points where the liner(t) = 4 − 3t, 8 + 7t, 5 + t, −∞ < t < ∞,intersects each of the…

A: The point where the line intersects co-ordinate planes, one of the co-ordinates must be zero.

Q: Find the point at which the line intersects the given plane.

A:

Q: Discussion: 1- Show that Ramp(t) = u(t) dr = t * u(t)

A: The ramp function is very significant function in mathematics. It is the composition of two…

Q: Find the equation for the plane through Po(4,9,8) perpendicular to the following li x= 4+t, y = 9+…

A: Given x=4+t  , -∞<t<∞y=9+2tz=-5tx=t=x-41 , y=t=y-a2  , z=t=-z5

Q: Find the equation of the set of points located three units away from the plane -2х + бу + 3z + 1…

A: Given equation of the plane, -2x+6y+3z+1=0

Q: Find the distance between the given parallel planes. 2x- 2y +z = 10, 4x-4y+2z= 1 4x – 4y+2z = 1 19…

A:

Q: The midpoint of \overline{\text{AB}}AB is M(0, -4)M(0,−4). If the coordinates of AA are (-8,…

A: Given Data: The midpoint of AB¯ is: Mxm, ym=M0, -4 The coordinates of A is: Axa, ya=A-8, -7 Let The…

Q: Think of a parallelogram made with cardboard strips and hinged at each vertex so that the measure of…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 800 lb 800 lb 600 lb 600 lb 400 lb 3 ft- -3 ft -3 ft- -3 ft- 0.6 ft 1.2 ft 'A B 0.6 ft

A: Given,

Q: Find the midpoint of CD. M = (, X1+X2 _Yi+Y2 2 %3D C= (10,-1) and D = (-6,3) ([ ? ],[ ])

A: We can find the mid point of CD as below

Q: ind a plane containing the point Gl,2,-3) and the line of intersection of the pladnes -X+3y -Z E -7…

A:

Q: iven two line segments, construct a rhombus whose diagonals have lengths equal to the lengths of the…

A:

Q: 4) Name a point that is coplanar with A, B, and C. b. E D a. D d. N C. F 3)

A: the given figure we have to name a point that is coplanar with A, B and C.

Q: In Exercises 17-20, find the equation of the plane with the given description.18. Passes through (4,…

A: Solution:-  We have to  find the equation of the plane with the given description.18. Passes through…

Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below,…

A:

Q: To which coordinate plane is the plane y = 1 parallel?

A: y=1

Q: The midpoint of AB is M(0, –4). If the coordinates of A are (2, –1), what are the coordinates of B?…

A: Given- The midpoint of ABis M0,-4. To Find- The coordinate of point B, if the coodinate of the point…

Q: Name three points that determine plane M.

A: Given, two planes M and N that intersect on line passes through A and B in image we can see three…

Q: The midpoint of AB is M(2, –2). If the coordinates of A are (-2, 1), what are the coordinates of B?

A: Recall: Mid point Formula: The midpoint of M(x,y) of the line segment from A(x1,y1) to B(x2,y2) is…

Q: In Exercises 10–12, M is the midpoint of AB, where the coordinates of A are given. Find the…

A: Given1)A(4,-2)   M(4,4)2)A(1,-3)   M(5,1) 3)A(r,s)   M(0,2)  where M is midpoint. To find B in all…

Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: Given that the point (5, 0) a) symmetric with respect to the x axis Substitute the coordinate -y for…

Q: 5. What can you change to the two planes to make them parallel? Make as few changes as possible and…

A: given planes π5: 2x-4y+2z-2=0π6: x-y+3z-2=0

Q: Find the value of x and y for which OCARE is a parallelogram. b. C 4x+3 A a. C A 2y ROE 5x-4 R R…

A:

Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

A:

Q: Determine the point of intersection of the line and the plane. e:[x, y, z]= [3, 1, 2]+t[1, -4, -8]…

A: Finding the general point in the line substituting in the equation of a plane

Q: 2. B C. a. Which pair(s) of planes intersect? b. Which planes intersect in RS ?

A: 2 a.  The pairs A,C and B,C are the intersecting planes. The planes A and C intersect as; The planes…

Q: The midpoint of \overline{\text{AB}}AB is M(1, 1)M(1,1). If the coordinates of AA are (-2, 5)(−2,5),…

A: Given, A=(x1,y1)=(-2,5) Midpoint M(1,1) Let the other point B have coordinates (x2,y2)

Q: A plane can be determined by points, that are not on the same line. OA. unable to be determined OB.…

A:

Q: Write an equation for the plane that contains the x-axis and the point (0, 8, 24). O 3 = x² + y? +…

A: Please refer the attached image for complete solution.

Q: 1. Which of the following points in the standard (x, y) coordinate plane is farthest from the…

A: Which of the following  points in the standard (x, y) coordinate plane is furthest from the origin

Q: Find the midpoint of CD. M = ( X1+X2 Yı+y2 C = (10,-1) and D = (-6,3) %3D %3D ([ ? ],[ ])

A: Use the given mid point formula and simplify.

Q: 1. Rhombus ABCD with vertices A(-3, -2), B(0, 3) C(5, 6), and D(2, 1): (x, y) → (x + 2, y-6) A'L B'…

A: The given coordinates of rhombus is  A-3,-2, B0,3, C5,6, D2,1 The transformation is x,y→x+2,y-6 So…

Q: While the coordinate axes separate the Cartesian plane into 4 subsets (quadrants), the xy plane, z…

A: given

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Consider the Voronoi diagram below for a city that contains the towns A, B, C, and D. The equation…

A:

Q: The midpoint of AB is M (0, –4). If the coordinates of A are (-8, –7), what are the coordinates of…

A: To find the coordinate of point B. If the coordinate of point A and midpoint of line AB is given.

Q: Y. 14 12 10 8 6 D. --4-2 2. 6 8 10 12 14 A 4. 2. 4.

A: from midpoint formula

Q: 2. The midpoint of AB is M(4,2). If the coordinates of A are (6,-4), what are the coordinates of B?…

A: Since, we have been given that the midpoint of AB is M(4,2) and coordinates of A(6,-4). Then Our Aim…

Q: The midpoint of \overline{\text{AB}}AB is M(-5, -2)M(−5,−2). If the coordinates of AA are (-3,…

A: Topic- 2D Geometry

Q: The midpoint of AB is M(5, -2)M(5,−2). If the coordinates of AA are (6, -5)(6,−5), what are the…

A: Mid point of a line joining two points(x1, y1) and  (x2, y2) is given byMid point = x1+ x22,y1+ y22

Q: Given that A and B are parallel to the yz plane, that |A| = 2, |B| = 4, and A • B = 0, what can you…

A: Consider the provided question, Given A and B are parallel to the yz plane.

Q: The midpoint of AB is M(1,3). If the coordinates of A are (-1, 5), what are the coordinates of B?

A:

Q: Name a fourth point that is in the same plane as the given points. 11. A, B, C 14. A. D, E 12. E. F.…

A: The point D is on the same plane as A, B, C. The point H is on the same plane as A, D, E. The point…

Q: In Exercises 41-44, find the intersection of the line and the plane.44. X - Z = 6, r( t) = ( 1, 0,…

A:

Q: The midpoint of AB is M(1, 3). If the coordinates of A are (-1, 5), what are the coordinates of B?

A: