Question

Check if (3,6), (3,4) and (5,4) form an isosceles right angled triangle.​

Answer 1

S O L U T I O N :

Let,

• R(3,6)
• A(3,4)
• J(5,4)

Applying distance formula,

Distance between two points = √(x2 - x1)² + (y2 - y1)²

Case (I), R(3,6) & A(3,4)

[ Put the values in distance formula ]

=> RA = √(3 - 3)² + (4 - 6)²

=> RA = √(0)² + (-2)²

=> RA = √0 + 4

=> RA = √4

=> RA = 2 Units ------(1)

Case (II), A(3,4) & J(5,4)

[ Put the values in distance formula ]

=> AJ = √(5 - 3)² + (4 - 4)²

=> AJ = √(2)² + (0)²

=> AJ = √4 + 0

=> AJ = √4

=> AJ = 2 Units --------(2)

Case (III), R(3,6) & J(5,4)

[ Put the values in distance formula ]

=> RJ = √(5 - 3)² + (4 - 6)²

=> RJ = √(2)² + (-2)²

=> RJ = √4 + 4

=> RJ = √8

=> RJ = 2√2 Units -------(3)

From equation (1) & (2),

=> RA = AJ

Hence,

.°. ΔRAJ is an isosceles right angled triangle.

Therefore,

Point A(3,6), B(3,4) and C(5,4) form an isosceles right angled triangle.

Answer 2

$\huge{\boxed{\rm{Question}}}$

Check if (3,6) ; (3,4) and (5,4) form an isosceles right angled triangle.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• Some digits are given like that (3,6) ; (3,4) and (5,4)

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Check that the given form an isosceles right angled triangle.

$\large{\boxed{\boxed{\sf{Solution}}}}$

Note : See full answer to know it properly.

$\large{\boxed{\boxed{\sf{Assumptions}}}}$

• A(3,6)

• B(3,4)

• C(5,4)

$\large{\boxed{\boxed{\sf{Using \: formulas}}}}$

• Formula of Distance =

√(x2 - x1)² + (y2 -y1)²

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that we have to check that the given numbers form an isoscles right angled triangle. The digits are as (3,6) ; (3,4) and (5,4).

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question we have to use our assumptions. Afterwards using the formula of distance that is √(x2 - x1)² + (y2 -y1)². After that seeming the cases, Case 1 we have to out the values (continuing....) we get our equation 1 afterthat seeming case 2 we have to put the values (continuing....) we get our equation 2 afterthat seeming case 2 we have to put the values we get equation 3 hence, it's checked that ∆ABC is an isoscles right angled triangle.

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

According to the question we already know that what to do means what is given or what to check.

So, using the taken assumptions,

We have to use th formula of distance that is√(x2 - x1)² + (y2 -y1)².

Let's carry on to the question,

Cᴀsᴇ (１) A(3,6) ; B(3,4)

Putting the values we get the following results,

➝ AB = √(3-3)² + (4-6)²

➝ AB = √(0)² + (-2)²

➝ AB = √0 + 4

➝ AB = √4

➝ AB = 2 Eǫᴜᴀᴛɪᴏɴ ❶

Cᴀsᴇ (２) B(3,4) ; C(5,4)

Putting the values we get the following results,

➝ BC = √(5-3)² + (4-4)²

➝ BC = √2² + (0)²

➝ BC = √4 + 0

➝ BC = √4

➝ BC = 2 Eǫᴜᴀᴛɪᴏɴ ❷

Cᴀsᴇ (３) A(3,6) ; C(5,4)

Putting the values we get the following results,

➝ AC = √(5-3)² + (4-6)²

➝ AC = √(2)² + (-2)²

➝ AC = √4 + (-4)

➝ AC = √4 + 4

➝ AC = √8

➝ AC = 2√2 Eǫᴜᴀᴛɪᴏɴ ❸

Now, what to do ?

Oh... From Eǫᴜᴀᴛɪᴏɴ ❶ and Eǫᴜᴀᴛɪᴏɴ ❷

➝ AB = AC

Henceforth, it's checked.

∆ABC is an isosceles right angled triangle.