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Chapter 10: Q. 5TB (page 777)

The distance between two points in the plane: What is the formula for computing the distance between points \(\left ( x_{1},y_{1} \right ) and \left ( x_{2},y_{2} \right )\)?

Short Answer

Expert verified

The formula for computing the distance between points \(\left ( x_{1},y_{1} \right ) and \left ( x_{2},y_{2} \right )\) is

\(\sqrt{\left ( {x_{2}-x_{1}} \right )^{2}+\left ( y_{2}-y_{1} \right )^{2}}\).

Step by step solution

01

Step 1. Given Information

The given points are \(\left ( x_{1},y_{1} \right ) and \left ( x_{2},y_{2} \right )\) .

We have to find the formula for the distance between two points in the plane.

02

Step 2. Find the distance between two points in the plane

To find the distance between two points in the plane where the points are \(\left ( x_{1},y_{1} \right ) and \left ( x_{2},y_{2} \right )\). Then the formula to find the distance between two points is given:

\(\sqrt{\left ( {x_{2}-x_{1}} \right )^{2}+\left ( y_{2}-y_{1} \right )^{2}}\).

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Most popular questions from this chapter

In Exercises 22–29 compute the indicated quantities when u=(2,1,−3),v=(4,0,1),andw=(−2,6,5)

role="math" localid="1649400253452" (u×v)×wandu×(v×w)

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(1,4,6),Q(−3,5,0),R(3,2,−1)

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is k=1.

(b) True or False: ∑k=0n 1k+1+∑k=1n k2is equal to ∑k=0n k3+k2+1k+1.

(c) True or False: ∑k=1n 1k+1+∑k=0n k2is equal to ∑k=1n k3+k2+1k+1 .

(d) True or False: ∑k=1n 1k+1∑k=1n k2 is equal to ∑k=1n k2k+1.

(e) True or False: ∑k=0m k+∑k=mn kis equal to∑k=0n k.

(f) True or False: ∑k=0n ak=−a0−an+∑k=1n−1 ak.

(g) True or False: ∑k=110 ak2=∑k=110 ak2.

(h) True or False: ∑k=1n ex2=exex+12ex+16.

In Exercises 30–35 compute the indicated quantities when u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)

role="math" localid="1649434688557" v×wandw×v

In Exercises 30–35 compute the indicated quantities when u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)

u×wandw×u
See all solutions

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