Question

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Answer 1

Any ideas?

Answer 2

29^1/2 for the first one?

Answer 3

So we calculate the length of each side and see which one is the greatest... that's what you did I guess ?

Answer 4

Yeah was that right....

Answer 5

Remember to use distance formula:

Distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Answer 6

I'm hella confused now. Ugh

Answer 7

Now, if you calculated each side... you can answer what type of triangle is ABC...

If every side is equal ... it is equilateral

If only two sides are equal ...it is isosceles

And if no side is equal... it's scalene

Answer 8

Okay then let me start from beginning....

Answer 9

First let us calculate side AB...

We have A = (1,7) and B = (-2, 2)

Now, to calculate length of side AB, we calculate distance between points A and B...

Answer 10

This much is fine?

Answer 11

Hold on lemme go get calc.

Answer 12

Take your time

Answer 13

okay so do you add? subtract?

Answer 14

Naah.. to calculate the distance between two points we use the distance formula... now I will show how you use it to find AB... then you try to find out AC and BC... okay?

Answer 15

Yeesssir/mam not trying to be disrespectful but i cant tell. :)

Answer 16

It's fine :) Just call me Vishu .. no sir required :)

Answer 17

OKay thanks Vishu

Answer 18

Okay so we have here...

A = (1,7) and B = (-2, 2)

Now recall what I told you about distance formula...

distance between \((x_1, y_1)\) and \((x_2, y_2)\) = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

So, if I want to find out distance between (1, 7) and (-2, 2) then:

\(x_1 = 1\)
\(y_1 = 7\)
\(x_2 = -2\)
\(y_2 = 2\)

Any doubt till this step?

Answer 19

so substitue?

Answer 20

Now... I will just plug in the values in the formula...

So,

\(\text{AB} = \sqrt{(-2 - 1)^2 + (2 - 7)^2}\)

\(\implies \text{AB} = \sqrt{(-3)^2 + (- 5)^2}\)

Answer 21

Now we just simplify this more..

\(\implies \text{AB} = \sqrt{9 + 25}\)

\(\implies \text{AB} = \sqrt{34}\)

Answer 22

So this is how we will be finding the sides of the triangle... any doubt?

Answer 23

No but dont understand how that is going to help me fill in blanks?

Answer 24

See... first we will find out the length of each side of the triangle.. once we know the sides... we can easily say which one is the longest side... This will be the first answer.

Also, if you know all the sides you can tell whether it is an equilateral triangle, isosceles triangle or a scalene triangle.. That will be the answer to second blank.

For third and fourth part, we will have to calculate AD, BD and CD... then again, once we know all the sides, we can tell what type of triangle ABD will be and what will be the length of side AD.

Answer 25

okay, how do we go about this?

Answer 26

Now that's the interesting part :) Now, using how I calculated side AB, try to find out AC...

Answer 27

If you have any doubt at any step.. feel free to ask.. and if you get the length of side AC.. do let me know and we will move forward

Answer 28

You deleted the formuka, What was it again?

Answer 29

Here it is:

Distance between points \((x_1, y_1)\) and \((x_2, y_2)\) = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Answer 30

Correct me if im wrong but is it squareroot 34?

Answer 31

Wonderful!!!

Answer 32

Perfectly correct :D

Answer 33

Yay.

Answer 34

Now can you calculate BC ?

Answer 35

Yesss give me a minute

Answer 36

Sure take your time :)

Answer 37

Squarerooot 36?

Answer 38

Great job!!

Answer 39

Now so we have the sides to be AB = AC = sqrt(34) and BC = sqrt(36)

Answer 40

So which side is the longest side?

Answer 41

BC?

Answer 42

Great going :D

Answer 43

Perfect!!

Answer 44

Now, recall what I told you about type of triangles...

1. If all sides equal => equilateral triangle
2. If only two sides equal => isosceles triangle
3. If all sides are different => scalene triangle

So what type of triangle is ABC?

Answer 45

thats not an answer option.. :(

Answer 46

and scalene.

Answer 47

Naah naah...

First thing first..

What is the square root of 36? (The answer is one of the option)

Answer 48

ohh okay its 6 hahaaa.

Answer 49

:) Good

Answer 50

Is it a scalene?

Answer 51

No... See you calculated the sides... two had the length sqrt (34) and one had length 6 units... So, how many sides have equal length?

Answer 52

oh only 2! so isosceles?

Answer 53

Exactly!! Very nice

Answer 54

Now, shall we move on? Now, for the last two parts... we have a different triangle so a different set of sides...

So, can you calculate AD?

Answer 55

Remember that point A is the same as before i.e. (1,7) and D is (1,2)

Answer 56

okay give me a minute.

Answer 57

Sure!

Answer 58

25?

Answer 59

square root of it ;)

Answer 60

Very good... so we found out AD = sqrt(25) ... what about BD and CD? Can you calculate them..?

Answer 61

c and what?

Answer 62

First length of BD... B is (-2, 2) and D is (1,2)

Answer 63

9

Answer 64

Don't forget the square root :)

Answer 65

Yes too much trouble to type that out hahaa.

Answer 66

So, length of BD = sqrt(9)

What about CD... ? C = (4,2) and D= (1,2)

Answer 67

Thats 9 aswell.

Answer 68

Very nice!!

Answer 69

So how many sides are equal in this triangle.. ?

Answer 70

2

Answer 71

Very nice!! So what type of triangle is this?

Answer 72

isosceles?

Answer 73

Very very good :)

Answer 74

So,...what is the length of AD ?

Answer 75

and the last one is 5 am i correct?

Answer 76

Exactly!!!

Answer 77

So.. here you go :) You solved the whole problem by yourself :)

Answer 78

No actually i had help thank you so much nobody can ever get through to me. i will be messaging you if i need help again is that okay?

Answer 79

That's fine :)