Question

Find the circumcentre of the triangle whose vertices are (1,3),(-3,5)and(5,-1)
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Answer 1

Answer:

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Answer 2

Answer:

The circumcentre of the triangle with vertices $(1,3),(-3,5)$ and $(5,-1)$ is $(-8,-10)$

Step-by-step explanation:

Given:

vertices of the triangle are $(1,3),(-3,5)$ and $(5,-1)$

We need to find the circumference of the triangle

Let the circumference of the triangle be $(x,y)$

The distance from the vertices to the circumcenter is equal so

Lets equate any two vertices

The we get the equation as

$(x-1)^2+(y-3)^2=(x+3)^2+(y-5)^2\\\\-2x+1-6y+9=6x+9-10y+25\\\\8x-4y+24=0\\\\2x-y+6=0$-- eq(1)

The other two vertices we get as

$(x-1)^2+(y-3)^2=(x-5)^2+(y+1)^2\\\\-2x+1-6y+9=-10x_25+2y+1\\\\8x-8y-16=0\\\\x-y=2$

Putting $y=x-2$ in 1 we get

$2x-x+2+6=0\\\\x=-8\\\\y=-10$