Question

please find solutions​

Answer 1

$\sf{Answer}$

Step by step explanation:-

Concept to know for solving this questions :-

Three points you have to keep in your mind :-

The centroid divides Orthocentre and circumcentre internally in ratio of 2:1 By using this ratio and by using section formula We can find the unknown cordinates

Nine point centre is the mid point of Orthocentre and circumcentre Then we can find The co-ordinates of Nine point centre by using mid point formula

Formulae required for solving this

• Mid point formula
• Section formula
• Centroid formula

Mid point formula :-

$\sf\dfrac{x_1 +x_2}{2}$, $\sf\dfrac{y_1+y_2}{2}$

Section formula:-

$\sf\dfrac{mx_2+nx_1}{m+n}$, $\sf\dfrac{my_2+ny_1}{m+n}$

Centroid formula:-

$\sf\dfrac{x_1+x_2+x_3}{3}$,$\sf\dfrac{y_1+y_2+y_3}{3}$

Distance formula :-

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

Note:-

For equilateral triangle Centroid, orthocentre, circumcentre equal

How to find the given triangle is a Equilateral triangle, Isoceless triangle , Right angle isoceless triangle

Equilateral triangle :- The distance b/w three sides are equal

Isoceless triangle :- The bistance b/w 2 sides are equal

Right angle triangles :- The distance b/w the points should satisfies pythogares theoram

For right angle triangle ,

Circumcentre = mid point of hypotenuse

Orthocentre = At right angle triangle

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