3. Given a line and a plane in three dimensional space, what are all the possible ways they can intersect?

Q: A snowman with the radius of 4 units and 6 units is standing on the third quadrant of the Cartesian…

A: The given graph is as follows:

Q: Must three parallel lines be coplanar? Draw a diagram to illustrate your answer.

A: To write: Three parallel lines be coplanar or not and to draw the diagram.

Q: Consider noncollinear points A, B, and C. If each line must contain two of the points, what is the…

A: Given- Three noncollinear points A,B and C. If each line must contain two of the points . To find-…

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: Give an example of three planes,exactly two of which are parallel.

A: Give an example of three planes,exactly two of which are parallel.

Q: 1. quadrilateral TUVW with vertices T(-3, -8), U(-6, 3), V(0, 3), and W(3, 0); translate by (4, 5)

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

Q: 1. Quadrilateral ABCD with vertices A(-4, 1), B(-2, 3), C(0, -2), and D(-5, -2): k = 3 A'L B'( C'(L-…

A: We are given with the vertices of quadrilateral  and need to plot the graph.…

Q: Suppose that (a) point C lies in plane X and (b) point D lies in plane X. What can you conclude…

A: Let point C and D lies in plane X. A straight line can be formed by joining the points C and D. Let…

Q: Chas vertices A(1: 3): B(4: 1) and C(6: 4), Prove that

A:

Q: ( , s) Let A = (-1,3) and B = (2, 4). Find the set of points C such that the area of triangle ABC is…

A:

Q: Prove a quadrilateral with vertices G(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle. 34 ES 10

A:

Q: Which of the following is/are axiom/s in projective geometry? I. All the points of the plane belong…

A: We have to determine which of the following is axiom of projective geometry.

Q: If a point (a,b) is a point in the coordinate plane, what will its location be after it has been…

A: Find your answer below

Q: Suppose that (a) points A, B, and C are collinear and (b) AB > AC. Which point can you conclude…

A: (a) A, B and C are collinear⇒ A, B and C lie on a straight line

Q: Prove that a quadrilateral with vertices J(2,-1), K(-1,-4), L(-4,-1), and M(-1,2) is a square.

A: We have to prove that the quadrilateral given is a Square

Q: Is Span({(4,–10, 6), (-6, 15,–9)}) a line or a plane in R³? Why?

A:

Q: What are the coordinates of the point on the directed line segment from (-8,-2) to (6, 2) that…

A:

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

A:

Q: Prove that if two lines are each perpendicular to a third line in the plane, then the two lines are…

A: Let slope of two lines are m1 and m2 and slope of third line is m3 . Now, as both lines are…

Q: 2. Show that the points A(2,2,2), B(2,0,1), C(4, 1, – 1) and D(4, 3,0) are coplanar and that they…

A: The solution are next step

Q: consider noncollinear points A, B, and C. If each line must contain two of the points, what is the…

A: Given:The noncollinear points A, B, and C.

Q: Enter a whole number. To tessellate a plane with squares, hexagons, and dodecagons, one needs…

A: Tessellate a plane with the given figure means joining the given figure number of times to get the…

Q: Given two planes, discuss the various possibilities for the set of points they have in common. Then…

A:

Q: 10 11 3 vertices at a parallelograni AaCD are shown in the appiet What are the coordinates of point…

A:

Q: Which of the following is/are axiom/s in projective geometry? I. All the points of the plane belong…

A: We have to determine which of the following is axiom of projective geometry.

Q: Consider the following figure. A quadrilateral has four labeled vertices, three labeled angles, and…

A: Given description of the quadrilateral is The left side starts at vertex A, travels down and to the…

Q: Prove without using the concept of duality: In the four-line geometry, there exists a pair of points…

A:

Q: Suppose that four lines in a given plane a1, a2, b1. bz are given, with the conditions (also given)…

A:

Q: can a given line be in a two planes?in ten planes?

A: Yes,             The given statement is true;     A line can be drawn in a two planes ;…

Q: If this trapezoid is moved through the translation (x+3, y-2), what will the coordinates of B' be?

A:

Q: Three noncollinear points determine three lines, as was shown in Figure 9.2. (a) How many lines are…

A: Given- Four points, five points and n-points. To find- The number of lines formed by above points.…

Q: What are the coordinates of the point on the directed line segment from (-6,-6) to (9,-1) that…

A:

Q: What are the coordinates of the point on the directed line segment from (-10,-5) to (5,1) that…

A:

Q: 4. The coordinates of the vertices of a quadrilateral are P(1, 2), R(1, 4), S(3, 4) and 7(4, 2).

A: The coordinates of the vertices of a quadrilateral are P(1,2) , R(1,4) , S(3,4) and T(4,2) according…

Q: Prove that quadrilateral DAVE with the vertices D(2,1), A(6,-2), V(10,1), and E(6,4) is a mbus. Yt…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Solve the following problems completely. If there are seven distinct points on a plane with no…

A: Given: Total number of points is, n=7. No three points are collinear. The objective is to find the…

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: Which of the following statements is/are not true about non-Euclidean geometries? I. In…

A: We will use basic definition to answer this question

Q: 3. Mr. Cruz would like to buy a lot however, his broker gave the dimension of the lot using the…

A: The area of a quadrilateral when 4 of its vertices in counter-clockwise direction0 is:…

Q: If A, B, C, and D are collinear, then they lie in the same plane. A, B, C, and D lie in the same…

A:

Q: erify that the points are the vertices of a parallelogram, and find its area. А(1, 1, 3), В(3, -5,…

A: We have to find area

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: 14. How many straight lines can be formed by joining 12 points on a plane out of which no points are…

A:

Q: If there are 9 distinct points on a plane, no 3 of which are collinear, how many quadrilaterals can…

A:

Q: 6. JaMarcus claims that (2,1) is the point of intersection of the lines y = 5x-3 and y=-4x+6. Is he…

A:

Q: 5. Given 3 points in space, is there always a plane that passes through all of them? What if…

A: Let us consider three points A=x1,y1,z1 , B=x2,y2,z2 , C=x3,y3,z3. Then, if a plane passes through…

Q: The letters A and B are topologically equivalent. True False

A: To determine the letters A and B are topologically equivalent or not

Q: 3. Given two planes, discuss the various possibilities for the set of points they have in common.…

A: Given that,  two planes, the number of possibilities  for the set of points. There are following…

Q: Does a plane have edges?

A: A plane is infinite by the notion. So it does not have an edge.

Q: 1) What's another term for translating an object on the coordinate plane?

A: Another term for translating an object on the coordinate plane is ISOMETRY. Usually ISOMETRY is also…