Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Let $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$ be in any two points in the plane. (a) Plot these points, (b) Obtain the right triangle formed by drawing a horizontal line from $A$ and a vertical line through $B$. What are the coordinates of the point at which these two lines intersect? (c) Using the theorem of Pythagoras, derive the distance formula.

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Oregon State University

McMaster University

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

03:18

02:35

Let $\left(x_{1}, y_{1}\ri…

02:34

Use the figure, which show…

01:46

Find the distance between …

01:11

02:41

03:34

If the lines $a_{1} x+b_{1…

01:21

A pair of points is graphe…

01:19

Let $a x+b y+c z=d$ be the…

for this problem, We're going to plot to generic points A and B. Now, we don't know anything about their coordinates. We don't know which quadrants there in. I'm just going to draw to random points. So let's call this one a and I'll call this point over here, we'll call. That be, um I am not going to assume anything about oh, where the points are if they're positive or negative. I'm not gonna be physically counting because I want this to be a generic, uh, experience here that we're going to dio. So here are my A. It might be the A. The coordinates are X one Y one B has the coordinates X two y two. So what we're going to do now is I'm going to draw a right triangle. I'm gonna do a horizontal line from a and a vertical line from B, and then I can connect those two points. So here we have a right triangle, so we're going to call the point where they meet. Let's call that point C. Well, what is point see? So if I want to do see and write down its coordinates, well, it shares the same X coordinate as B. So the X coordinate for C is x two and it shares the same. Why coordinate is a So that is why one. So those were those were my two points and the point where those lines are going to meet. Now, what I want to dio is we're gonna use these three points to derive the distance formula. So I'm gonna call the distance between A and B. That is D. That's the distance. So what is the distance? Well, the Pythagorean theorem says that the hypotenuse in this case d d squared equals the sum of the legs squared. So I'm going to call. I'm just gonna give us some little some variables here. Let's call that leg l in that leg am so on. My Pythagorean theorem d squared equals l squared plus m squared. Well, let's see what is L squared while l squared is the distance between C and B. The X coordinates the same. I'm just counting the wise. What's the difference in the wise? Any time in math that you're talking about difference? That's a subtraction. So I could do this is why one minus y two squared because I'm squaring it. It doesn't matter which order I put this in. If I have why one minus y two y tu minus. Why one? No matter if that's a positive or negative value when I square it, it's going to be a positive number. So that l squared is why one minus y two squared MM is the distance between points C N A. And for those they share the same. Why value? So the difference. The distance is just the difference in the exes. So I could do the same thing here and again by squaring it. I don't have to about which of these is bigger, which one smaller I square is. Give me a positive value. And finally, if I want just the distance, I'm going to take the square root of both sides. Right? And this gives me my distance formula. The difference of my wise square, the difference of my exes squared. Add those together and take the square root

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:59

Use the first derivative to determine where the given function is increasing…

02:10

Determine the coordinates of the midpoint of the line segment joining the po…

01:06

You are given a pair of supply and demand equations; identify which is suppl…

01:16

01:04

The maximum possible demand for a certain commodity is 20,000 tons. The high…

01:13

Find the average rate of change of $y$ with respect to $x$ on the given inte…

02:07

(a) Find the $x$ -intercept(s); (b) Find the vertical asymptotes; (c) Find t…

01:23

Locate all critical points.$$r(x)=4 x^{3 / 4}+2$$

01:36

Show that the graph of the function defined in Example 12 does not cross its…

02:01

Decide whether or not the function is continuous. If it is not continuous, i…