The amazing quadrilateral property—coordinate free The points P, Q, R, and S, joined by the
- a. Use vector addition to show that u + v = w + x.
- b. Let m be the vector that joins the midpoints of PQ and QR. Show that m = (u + v)/2.
- c. Let n be the vector that joins the midpoints of PS and SR. Show that n = (x + w)/2.
- d. Combine parts (a), (b), and (c) to conclude that m = n.
- e. Explain why part (d) implies that the line segments joining the midpoints of the sides of the quadrilateral form a parallelogram.
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter 13 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
Precalculus
Glencoe Math Accelerated, Student Edition
Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- please solve in matrix form (computer graphics) Translate object ABCD with co-ordinates A(0, 0, 0), B(3, 0, 0), C(3, 3, 3), D(0, 3, 0) by 2 units in all direction and then scale it by 1 units in x direction and - units in y direction and no change along z-direction about (1, 2, 1). 4arrow_forward3) Show that the set of three-dimensional coordinates {(x, y, z)|x, y, z E Z} has size equal to N.arrow_forwardGiven A = {1,2,3} and B={u,v}, determine. a. A X B b. B X Barrow_forward
- If there are two equal angles in a given triangle, then their corresponding opposite sides must be equal.arrow_forwardThis problem is on Computer Graphics and is based on the topic 'Perspective Projection'. Please provide a step-by-step solution to the problem and explain the steps. The solution must include the General purpose perspective projection matrix. Question: Let a 3D point (423, -423, 423) be projected on a projection plane. Given that the center of the projection plane is (0.0, 0.0, -423.0) and the coordinate of the COP is (4, 2, 3). Determine the coordinate of that 3D point on the projection plane using a general purpose perspective projection matrix.arrow_forwardLet l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂arrow_forward
- Let A={3,5,7,9}, B={2,3,5,6,7}, and C={2,4,6,8} be all subjects of the universe U={2,3,4,5,6,7,8,9}. Find (a) The union of A and B; (b) The intersection of B and C; (с) АӨВ; (d) В Х С (e) A \ B (f) P(A) (g) The complement C° of the set C; (H) The complement of U.arrow_forwardWrite a program that can inverse a matrix by using an approach to find its minor, cofactor and adjugate matrix. Test your program with the given matrix ? Please provide in Python programarrow_forwardImagine a 3D plane P in your 3D scene. An infinite number of lines can lie on that plane. Consider one set of parallel lines on this 3D plane. This set will produce one vanishing point when projected on the image plane. Consider now all possible sets of parallel line on the plane P. What is the locus of all vanishing points produced by all sets of parallel lines? [Note that you do not have to right down a formula in order to solve this. You need to use a geometric argument.]arrow_forward
- Suppose that the equation ax b .mod n/ is solvable (that is, d j b, whered D gcd.a; n/) and that x0 is any solution to this equation. Then, this equation has exactly d distinct solutions, modulo n, given by xi D x0 C i.n=d / fori D 0; 1; : : : ; d 1arrow_forwardYou are a computer research scientist at Tesla, and your task is to create a computer vision application for self-driving cars to detect object and avoid collision. You know that Graham's scan is a method of computing the convex hull of a finite set of points in the plane. You decide to apply this algorithm to achieve the goal of your task. a) Suppose Graham's scan executes n points, where n >= 3. Prove that, at the end of the program, the stack S consists of, from bottom to top, exactly the vertices of convex hull in counter-clockwise order.arrow_forwardIf n points are connected to fom a closed polygon as shown below, the area of the polygon can be compuled as n-2 Area = (%)E (*»1 + x ) (y»1 - y ) =0 Notice that although the ilustrated polygon has only 6 distinct comers, n for his polygon is 7 because the algorithmexpects that the last point (x.ya) will be repeat of the initial point, (Ko.yo). Define a structure for a point. Each point contains x coordinate and y coordinate. The represe ntation of a Polygon must be an array of structures in your program. Write a C program that takes the number of actual points (n-1) from the user. After that, user enters x and y coordinates of each point. (The last point will be repeat of the initial point). Writo a compute Are a function which returns the area of the Polygon. Print he area of the Polygon in main. Display the area with wo digts after the decimal point. Note: The absolute value can be computed with fabs function. Example: double x.50: fabs(x) is 5.0 double x 0.0: fabs(x) is 0.0 double…arrow_forward
- Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
- C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
![Text book image](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780133976892/9780133976892_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337627900/9781337627900_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)