Question

Plot the points ( 0,-3) , ( 3,1) and ( 6,-3 ).what type of triangle is
Formed by joining them in pairs.

Answer 1

Given :

⠀⠀⠀⠀⠀⠀⠀Given points :-

• A(0 , -3)
• B(3 , 1)
• C(6 , -3)

To find :

Triangle formed by joining the points.

Solution :

To find the triangle formed by the points , first we have find the length of the sides of the triangle .

By using the Distance formula , we can easily determine the value of AB, BC and AC (According the diagram) !!

Length of AC :

Given Co-ordinates –

• (0 , -3)
• (6 , - 3)

Let the length of AC be x.

Using the Distance formula and substituting the values in it , we get :

$\boxed{\underline{:\implies \bf{l = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}}}}$

Here :-

• $x_{2}$ = 6

• $x_{1}$ = 0

• $y_{2}$ = -3

• $y_{1}$ = -3

$:\implies \bf{x = \sqrt{(6 - 0)^{2} + \{(-3) - (-3)\}^{2}}}$

$:\implies \bf{x = \sqrt{(6 - 0)^{2} + \{(-3) - (-3)\})^{2}}}$

$:\implies \bf{x = \sqrt{(6)^{2} + \{(-3) + 3)\}^{2}}}$

$:\implies \bf{x = \sqrt{(6)^{2} + \{(-\not{3}) + \not{3})\}^{2}}}$

$:\implies \bf{x = \sqrt{(6)^{2} + (0)^{2}}}$

$:\implies \bf{x = \sqrt{36}}$

$:\implies \bf{x = 6}$

$:\implies \bf{length\:(x) = 6\:units}$

Hence, the length of AC is 6 units.

Length of BC :

Given Co-ordinates –

• (3 , 1)
• (6 , - 3)

Let the length of BC be y.

Using the Distance formula and substituting the values in it , we get :

$\boxed{\underline{:\implies \bf{l = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}}}}$

Here :-

• $x_{2}$ = 3

• $x_{1}$ = 6

• $y_{2}$ = 1

• $y_{1}$ = -3

$:\implies \bf{y = \sqrt{(3 - 6)^{2} + \{1 - (-3)\}^{2}}}$

$:\implies \bf{y = \sqrt{(- 3)^{2} + (1 + 3)^{2}}}$

$:\implies \bf{y = \sqrt{(-3)^{2} + (4)^{2}}}$

$:\implies \bf{y = \sqrt{9 + 16}}$

$:\implies \bf{y = \sqrt{25}}$

$:\implies \bf{y = 5}$

$:\implies \bf{length\:(y) = 5\:units}$

Hence, the length of BC is 5 units.

Length of AC :

Given Co-ordinates –

• (0 , -3)
• (3 , 1)

Let the length of AB be z.

Using the Distance formula and substituting the values in it , we get :

$\boxed{\underline{:\implies \bf{l = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}}}}$

Here :-

• $x_{2}$ = 0

• $x_{1}$ = 3

• $y_{2}$ = -3

• $y_{1}$ = 1

$:\implies \bf{z = \sqrt{(0 - 3)^{2} + \{(-3) - 1\}^{2}}}$

$:\implies \bf{z = \sqrt{(-3)^{2} + (-3 - 1)^{2}}}$

$:\implies \bf{z = \sqrt{(-3)^{2} + \{(-4)\}^{2}}}$

$:\implies \bf{z = \sqrt{9 + 16}}$

$:\implies \bf{z = \sqrt{25}}$

$:\implies \bf{z = 5}$

$:\implies \bf{length\:(z) = 5\:units}$

Hence, the length of AB is 5 units.

Now , we get the Sides of the triangle as :-

• AB = 5 units
• AC = 6 units
• BC = 5 units

Here , two equal sides are there.

So , the triangle formed is an isosceles triangle !!