Question

Name the type of triangle formed by the points A (0, 4) , B (3, 0) , C (0, 0)

Answer 1

right triangle is formed.
C (0,0) has a right triangle

Answer 2

ABC forms a Right-angled triangle.

Given:

Points A (0,4) , B (3,0) and C(0,0)

To Find:

The type of triangle formed by the given points.

Solution:

We have to find the distance between each point to check the type of triangle.

Distance = $\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2}$

$AB=\sqrt{(3-0)^{2} -(0-4)^{2} }\\\\=\sqrt{9+16} \\\\=\sqrt{25} \\\\=5$

$BC =\sqrt{(0-3)^{2} +(0-0)^{2} } \\\\= \sqrt{9+0} \\\\= 3$

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

AB² = 5²=25

BC² =3²=9

AC² = 4²=16

Clearly, BC² + AC²=25=AB²

It follows the condition of the Pythagoras theorem.

∴ABC forms a Right-angled triangle.

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