2. Consider the points A(1, 1), B(4, 1), and C(1,5) in the Euclidean plane. In one Cartesian plane, draw AABC and its images under the following isometries: a. translation using the vector (-6, 2) b. reflection about the line y =-X c. O(-5), the rotation centered at the origin at an angle of – "For item 2, I need to see all four triangles in one plane only.

Q: Consider three points in three-dimensional space: ?=(11,2,−3),?=(2,−3,11),?=(−3,11,2) Let ? be the…

A: Let us consider the given points be To find the equation of plane containing the points A, B and C.…

Q: Q1) consider a plain (M) that contains the three points A(1,-1,1), B(2,3,0), and C(0,1,-2) a Find…

A: Given that A1,-1,1, B2,3,0, C0,1,-2 (a) The objective is to find the equation of the plane,…

Q: Given the points A(-6, -5,5) and B( −6, −5, 1). Question 3 a) Write parametric and symmetric…

A:

Q: Find the perpendicular distance from the point P(9, 6, 6) m to a plane defined by three points…

A:

Q: a) Consider the point R(1, -3,5) and the vector . If = SR, find the point fully labeled sketch…

A: Remember : AB→=OB⇀-OA⇀

Q: Which of the following statement(s) are TRUE for the line that passes through the point P(1,0, 3)…

A:

Q: 4. (a) Describe the three-dimensional coordinate system. What are the coordinate planes? (b) What is…

A: * As per our guidelines, we are supposed to solve only the first three problems/subdivisions. Please…

Q: Samantha says that a 180 degree rotation, with center P, has the same effect on points in the plane…

A: Topic = Geometry False

Q: 4. Points P(1, 2, 0), Q(2, 3, -1) and R(-1, 1, 5) lie on a plane. Find the Cartesian equation of the…

A:

Q: 16 ft. 8 ft. 22 ft. 12 ft. Suppose this is the shape of a swimming pool for which you must buy a…

A:

Q: QUESTION 20 Find the distance from the point (7, -14, -21) to the plane: 2x - 3y - 6z = 1

A: To find the distance from the point  (7, -14, -21) to the plane:   2x - 3y - 6z = 1

Q: ILLUSTRATION 4.58 Find the equation of the plane which contains the line of intersection of the…

A:

Q: If a line is parallel to the vector 4i + 10j + 7k and passes through the point P = (7,7,4), then the…

A: Solution

Q: 3. The point P=(-2, -3, 4) in R a. Draw the rectangular prism using the given point on the grid…

A:

Q: Three points with position vectors a, b, and c will be collinear (lie on a line) if the…

A: Given that:         Position vectors of points areA(2,2,3), B(6,1,5) and C(-2,4,3)

Q: 4. If the position vectors of the three points A, B and C are (2, 4, -1), (1, 2, -3) and (3, 1, 2)…

A:

Q: 29° 5.4

A: The given triangle is right triangle  We will apply tan to find x

Q: If a line is parallel to the vector 3i + 9j+ 6k and passes through the point P = (5, 5, 4), then the…

A:

Q: 6. Let P= (1,0,2), Q = (-2, 1, 1), R= (a, B,7) be points in R for real numbers a, B, and 7. (a)…

A: Given: Let us consider the given P=1,0,2, Q=-2,1,1, R=α,β,γ be points in ℝ3 for real numbers α,β,…

Q: 7. Lucas does not like Dustin weapon and decides to design his own. His model has a plane that…

A: Given that the plane contains the point A(-5, 2, -4) and two direction vectors, AB→=(4, 8, 1) and…