Question

Transformer show by using distance formula that a(-3,1) b(-5,-3) and c (-1,-3) form an isoceles triangle also find area.


pls give the step explanation thank u so much❤️​

Answer 1

Step-by-step explanation:

We know that the distance between the two points (x1,y1) and (x2,y2) is 

d=(x2−x1)2+(y2−y1)2 

Let the given vertices be A=(1,−3), B=(−3,0)and C=(4,1)

We first find the distance between A=(1,−3) and B=(−3,0) as follows:

AB=(x2−x1)2+(y2−y1)2=(−3−1)2+(0−(−3))2=(−4)2+(0+3)2=(−4)2+32=16+9

=25=5

Similarly, the distance between B=(−3,0) and C=(4,1) is:

BC=(x2−x1)2+(y2−y1)2=(4−(−3))2+(1−0)2=(4+3)2+12=72+12=49+1=50

=52×2=52  

Now, the distance between C=(4,1) and A=(1,−3) is:

CA=(x2−x1)2+(y2−y1)2=(1−4)2+(−3−1)

Here, since the lengths of the two sides are equal that is AB=CA=5, therefore, ABC is an isosceles triangle.

Now consider,

AB2+CA2=52+52=25+25=50=(52)2=BC2

Since AB2+CA2=BC2, therefore, ABC is a right angled triangle.

Hence, the given vertices are the vertices of isosceles right angled triangle.