Question

show the point (4,2) (3,1) and (2,3) are the vertices of isosceles triangle​

Answer 1

Step-by-step explanation:

if you have two coordinates p,q then you can

calculate distance between them by:

$\sqrt{ {( |px - qx| )}^{2} + {( |py - qy| )}^{2} }$

so like that we can find lengths of sides of this triangle.

length of 1st side is

$\sqrt{ { (|4 - 3| )}^{2} + {( | 2 - 1 | )}^{2} } = \sqrt{1 + 1} = \sqrt{2}$

length of 2nd side is

$\sqrt{ {( |3 - 2| )}^{2} + {( |1 - 3| )}^{2} } = \sqrt{1 + 4} = \sqrt{5}$

length of 3rd side is

$\sqrt{ {( |4 - 2| )}^{2} + {( |2 - 3| )}^{2} } = \sqrt{4 + 1} = \sqrt{5}$

2nd and 3rd side are equal that means that triangle they are forming is isosceles triangle.