Question

Find the incentre of the triangle formed by the points A (7,9)B(3,-7)and C(-3,3)

Answer 1

(1.7, 1.8) are the coordinates of the incentre of the triangle.

Step-by-step explanation:

Given that,

Coordinates of the triangle = A(7,9)  B(3,-7) and C(-3,3)

To find,

Incentre of the triangle =  {(ax1+bx2+cx3a+b+c)/p,(ay1+by2+cy3a+b+c)/p}

where x1, x2, and x3 are the x coordinates of the vertex

and y1, y2, and y3 are the y coordinates.

a, b, c is the triangles' sides and p would be the perimeter of the triangle.

Length of the side c = $\sqrt{(3 - 7) + (-7 -9)^{2} }$

= 16.5

Length of side a = $\sqrt{(-3-3) +(3 - (-7)^2$

= 11.7

Length of side b = $\sqrt{(-3-7) + (3 -9)^2}$

= 11.7

Thus, perimeter = a + b + c

= 16.5 + 11.7 + 11.7

= 39.9

Now, incentre = {(11.7(7)  + 11.7(3) + 16.5(-3))/39.9,  {(11.7(9)  + 11.7(-7) + 16.5(3))/39.9}

= (1.7, 1.8)

Learn more: Incentre of the triangle

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