In a classroom, 4 friends are seated at the points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, "Don't you think $\mathrm{ABCD}$ is a square?" Chameli disagrees. Using distance formula, find which of them is correct.

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Geometry

NCERT Class 10 - Math

Chapter 7

Coordinate Geometry

Section 1

Introduction

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Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Video Transcript

we are going to do problem number five. This question we have to just find whether the four points are making a it's quite an article. So the four points are something like this, You just saw it here roughly. So this is A B C D or E. So this point is A this is B. This is C. And this is deep. And if we join all this, this should give us a square were projects. So this for that, we need to find the distance between uh each point. Okay, like A B B C C D and Eddie. Now it is given in Cartesian Flynn in the book, so we can just find the corner cell by observing it carefully. So, A in this case is three comma four. Three comma four. B. In this case is six comma seven. See in this case is that has nine comma four. You have to just observe this in the book and read the points. This is simple. Nobody in this case is six commitment. Okay. Now, in order to be this, A B C. D. Has a square. What we need to progress and that maybe should be equals two. B. C. B C. Should be close to city. City should be castrated. They're simple. So to find the distance between any two point, we know the formula that D equals two. A little tough. X two minus X one Holy square plus. Why too minus Y one. Holy square. Okay, so this is the formula that we are going to use. So let's just fine for a B. So in this case A B uh next to and why why? To a six comma seven. So we'll be having this is six minus three Holy Square plus Y to Venezuelan. That is seven minus four. Holy square. So this is equals to six. Ministry is three, so three square is nine and seven minutes forests. Three. Then again, three squared is nine. So you're getting under out of 18 on the route of 18, which is equals two and that we can do it. It? S 300. This is the value of baby that we're getting. Now. Let's just find out the value busy again using the same formula here next to is nine. So this is nine minus six. Holy squared plus Y to Venezuelan. So this is four minutes seven holy squared. So nine minutes 63. So three square is again nine for Minnesota's ministry, Ministry square is nine. This will give us 9% that is 18. So again, this is a cost to three in the roof too. Let us find the city. Sit in this case again here using the same formula. So this is six minutes nine Holy square plus. That is why two minutes. Why? Even here? So this is one man is four. Holy square. So this is equals two six minutes. Uh nine, that is ministry is square, that is nine. So we write it as mine. One minute for that is ministry. Ministry squad is nine, This is nine plus nine, that is 18. So this is again 302. Now you can find the value of D. A. So this is equals two under Rudolf again using the same formula. So extreme in its X one s six minutes three only square plus. Why to Venezuelan? So this is one man. As for holy square, so so long it further to live six minutes three, that is three. So three squared is 91 minus four is three, so three squared is nine. So again this is equal to three under. So if you see all sides of equal, so this is a square. All sides are equal, so A B C. D is is quite, so A B C. D. Is uh square. So this is the answer in this case, that's all. Thank you.

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