Question

Help me with this Geometry question please!

Answer 1

isosceles

Explanation:

We first find the |TV| |VS| and |ST| of the triangle using the distant formula,

`d =\sqrt{{(x_1 - x)}^(2)+ {(y_1 - y)}^(2) }`

`|TV|=\sqrt{( {9 - 1)}^(2)+{(2-1)}^(2)}`

`|TV|=\sqrt{{8}^(2)+{1}^(2) }`

`|TV|=√(64+1)`

`|TV|=√(65)units`

`|VS|=\sqrt{({5- 9)}^(2)+{(8 -2)}^(2)}`

`|VS|=\sqrt{({ - 4)}^(2)+{6}^(2)}`

`|VS|=√(16+36)`

`|VS|=√(52)units`

`|ST|=\sqrt{({5-1)}^(2)+{(8-1)}^(2)}`

`|ST|=\sqrt{4^(2)+7^(2)}`

`|ST|=√(16+49)`

`|ST|=√(65)units`

It can be seen that |ST|=|TV|

This implies that the triangle has its two sides equal.

Therefore the triangle TVS is isosceles.

Note that scalene triangle has three nonequal sides whiles equilateral triangle has three equal sides.