Question

the triangle formed by the points (1,1)(4,1)and(1,5)is​

Answer 1

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The triangle formed by the points (1 , 1) , (4, 1), (1, 5) is________.

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Let, us name these points

A (1, 1)

B(4, 1)

C(1, 5)

Now finding the distance

AB, BC, AC

Using the distance formula

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

$AB = \sqrt{ {(1 - 4)}^{2} + {(1 - 1)}^{2} } \\ \\ AB= \sqrt{9 + 0} = 3 \: units$

$BC = \sqrt{ {(4 - 1)}^{2} + {(1 - 5)}^{2} } \\ \\ BC = \sqrt{9 + 16} \\ \\ BC = 5 \: units$

$AC= \sqrt{ {(1 - 1) + (1 - 5)}^{2} } \\ \\ AC = \sqrt{0 + 16} = 4 \: units$

Here, we can see that these sides are

3 units

4 units

5 units

it means it is a scalene triangle

but

3 , 4 , 5 are Pythagorean numbers

as

${5}^{2} = {4}^{2} + {3}^{2}$

It means the triangle formed by these sides will be a

Right angled triangle.