Use vectors to prove that the segments joining the midpoints of opposite sides of a quadrilateral bisect

Question:

Use vectors to prove that the segments joining the midpoints of opposite sides of a quadrilateral bisect each other (Figure 33). Show that the midpoints of these segments are the terminal points of

1 4 (2u+ v +z) and (2v + w+u) 1 4 u Z W V

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 27, 2023 08:26 AM

See More Questions

Team Project, Geometric ApplicationsTo increase your skill in dealing with vectors, use vectors to prove the following (see the figures)(a) The diagonals of a parallelogram bisect each other.(b) The...
The points P, Q, R, and S, joined by the vectors u, v, w, and x, are the vertices of a quadrilateral in R 3 . The four points neednt lie in a plane (see figure). Use the following steps to prove that...
Let ABCD be a general, not necessarily planar, quadrilateral in space. Show that the two segments joining the midpoints of opposite sides of ABCD bisect each other.
Suppose that a 20-year bond pays $4 coupon once a year, and its yield rate is 6%. The bond has write-down of $0.49 for the first year. Calculate the write-down amount for the third year. Round the...
Consider the distillation column shown in Figure. It would be reasonable to control the liquid level in the reflux drum, hD, by manipulating either reflux flow rate, R, or distillate flow rate, D....
Find the derivatives of the function. y = ln (sin 2 )
A circular current-carrying wire loop produces a magnetic field. A spinning disk of uniformly distributed charge produces a similar magnetic field. How would you expect the field due to a spinning...
Senora Company manufactures a single product that sells for $110 per unit. The company projects sales of 500 units per month. Projected costs are as follows: 1. Prepare a contribution margin income...
23. A convex mirror used for rear view on an automobile has a radius of curvature of 3m. If a bus is located at 5m from this mirror, find the position, nature and magnification of the image. 24. An...
Recall the following details about the two employees hired in November. a. CPP is deducted at 5.10% (considering $3,500 yearly exemption). b. EI is deducted at 1.62% of gross earnings. c. Both...
Prove that two nonzero vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0
We consider the equations of a line in symmetric form, when a 0, b 0, c 0. Find the symmetric equations of the line through P = (1, 1, 2) and Q = (2, 4, 0). 0x - x a y - Yo b 02-2 C
Oslo is the capital city of ________________________. a. Germany b. Canada c. Brazil d. Australia e. Norway
What is real estate investment analysis? How does it differ from the concept of market value?
What is net operating income (NOI)? What are after-tax cash flows? Why do real estate investors prefer to use ATCFs?
What is leverage, and what role does it play in real estate investment? How does it affect the riskreturn values of a real estate investment?
A football is thrown on a long pass. Compared to the balls initial horizontal velocity component, the velocity at the highest point is (a) greater, (b) less, (c) the same.
Briefly describe each of the following approaches to real estate market value: a. Cost approach b. Comparative sales approach c. Income approach
Two basic assumptions of technical analysis are that security prices adjust: a. Gradually to new information, and study of the economic environment provides an indication of future market movements....
Chris Zulliger was a chef at the Plaza Restaurant in the Snowbird Ski Resort in Utah. The restaurant is located at the base of a mountain. As a chef for the Plaza, Zulliger was instructed by his...
Complete the following steps for the given function, interval, and value of n. a. Sketch the graph of the function on the given interval. b. Calculate x and the grid points x 0 , x 1 , x n . c....
Compute the area of the region bounded by the graph of f and the x-axis on the given interval. You may find it useful to sketch the region. f(x) = 16 - x 2 on [-4, 4]
Use geometry (not Riemann sums) to evaluate the following definite integrals. Sketch a graph of the integrand, show the region in question, and interpret your result. [5 if x < 2 f(x) dx, where f(x)...
Express the function h(z) = f(g(x)) = in the form h(z) = (fog)(z) where f(x) and g(2) 2. a) g(z) b) f(z)
Yield to maturity The bond shown in the following table pays interest annually. (Click on the icon located on the top-right corner of the data table below in order to copy its contents into a...
1. Given a function f(t) = t- t2 over the interval 0 t. (a) Sketch a graph for the above function in the interval -3 < t <3 (b) Determine half range cosine series expansion. (c) Hence deduce that, 1...

Use vectors to prove that the segments joining the midpoints of opposite sides of a quadrilateral bisect

Question:

1 4 (2u+ v +z) and (2v + w+u) 1 4 u Z W V

Step by Step Answer:

We denote by A B C D the corresponding points in the figure and by E of ...View the full answer

Calculus

Students also viewed these Mathematics questions