Question

Do the point (3,2),(-2,-3) and (2,3) form a triangle

Answer 1

Answer:

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Step-by-step explanation:

Let the given points be,

⇒A(3,2),B(−2,−3) and C(2,3)

 

Therefore,

AB=(3+2)^2+(2+3)^2=50=52 units

BC=(−2−2)^2+(−3−3)^2=52=213 units

AC=(3−2)^2+(2−3)^2=2 units

 

Now, we can see that,

(2root13)^2=(5root2)^2+(root2)^2

BC^2=AB^2+AC^2

 

Therefore, the given triangle is a right angled triangle.

Answer 2

Answer:

• As the sum of any two sides of the lengths of these triangle is greater than the third length, the points P , Q , R form a triangle.

Step-by-step explanation:

Given

• (3,2) , (-2,-3) , (2,3)

To find

• Whether the given points form a rectangle or not

Solution

We have three sides, PQ , QR , PR, we shall find the distance for all the three sides using P , Q , R points where P(3,2) , Q(-2,-3) and R(2,3) are the given points.

PQ:

• √(-2-3)² + (-3-2)²
• √(-5)² + (-5)²
• √25 + 25
• √50
• 7.07 units

QR:

• √(2-(-2)² + (3-(-3)²
• √(4)² + (6)²
• √16 + 36
• √52
• 7.21 units

PR:

• √(2-3)² + (3-2)²
• √(-1)² + 1²
• √1 + 1
• √2
• 1.41 units

As the sum of any two sides of the lengths of these triangle is greater than the third length, the points P , Q , R form a triangle and all the sides of triangle are not equal.