Question

Show that, the points (-3, 1), (1, -2)
and (1, 4) are the vertices of an isos-
celes triangle​

Answer 1

Answer:

Step-by-step explanation:

Given,

A = ( -3 , 1 )

B = (1 , -2)

C = (1 , 4)

To Show :-

That these are Vertices of an Isosceles triangle.

Condition to Prove that Above points are Vertices of an Isosceles triangle :-

Show that two of it sides lengths are equal.

Solution :-

Calculating lengths of Sides :-

That is Distance b/w AB,AC,BC.

Distance formula :-

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

1) AB :-

$x_1 = -3,y_1=1\\x_2=1,y_2=-2$

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

$= \sqrt{16+9}\\\\= \sqrt{25}$

= 5 units

AB = 5units

2) BC :-

$x_1=1,y_1=-2\\\\x_2=1,y_2=4$

$BC=\sqrt{(1-1)^2+(4+2)^2}\\\\=\sqrt{6^2}$

= 6 units

BC = 6units

3) AC :-

$x_1=-3,y_1=1\\\\x_2=1,y_2=4$

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

$=\sqrt{16+9}\\\\=\sqrt{25}$

= 5units

AC = 5units

Since , we showed that AB = AC .

Hence Showed.