If line 3x + 3y -24 = 0 intersects x- axis at point A and y- axis at point B , then incentre of tria

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9.Straight Line

hard

If the line $3x + 3y -24 = 0$ intersects the $x-$ axis at the point $A$ and the $y-$ axis at the point $B$, then the incentre of the triangle $OAB$, where $O$ is the origin, is

$(3, 4)$

$(2, 2)$

$(4, 3)$

$(4, 4)$

(JEE MAIN-2019)

Solution

$I = \left( {\frac{{a{x_1} + b{x_2} + c{x_3}}}{{a + b + c}},\frac{{a{y_1} + b{y_2} + c{y_3}}}{{a + b + c}}} \right)$

$ = \left( {\frac{{8\left( {60} \right) + 6\left( 0 \right) + 10\left( 0 \right)}}{{24}},\frac{{10\left( 0 \right) + 6\left( 8 \right) + 8\left( 0 \right)}}{{24}}} \right) = \left( {2,2} \right)$

Standard 11

Mathematics

Let the equation of two sides of a triangle be $3x\,-\,2y\,+\,6\,=\,0$ and $4x\,+\,5y\,-\,20\,=\,0.$ If the orthocentre of this triangle is at $(1, 1),$ then the equation of its third side is

hard

(JEE MAIN-2019)

The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points $(a^2 + 1 , a^2 + 1 )$ and $(2a, – 2a)$, $a \ne 0$. Then for any $a$ , the orthocentre of this triangle lies on the line

hard

(JEE MAIN-2014)

The co-ordinates of the vertices $A$ and $B$ of an isosceles triangle $ABC (AC = BC)$ are $(-2,3)$ and $(2,0)$ respectively. $A$ line parallel to $AB$ and having a $y$ -intercept equal to $\frac{43}{12}$ passes through $C$, then the co-ordinates of $C$ are :-

normal

In a triangle $ABC$, coordianates of $A$ are $(1, 2)$ and the equations of the medians through $B$ and $C$ are $x + y = 5$ and $x = 4$ respectively. Then area of $\Delta ABC$ (in sq. units) is

hard

(JEE MAIN-2018)

The vertices of $\Delta PQR$ are $P (2,1), Q (-2,3)$ and $R (4,5) .$ Find equation of the median through the vertex $R$.

medium

If the line $3x + 3y -24 = 0$ intersects the $x-$ axis at the point $A$ and the $y-$ axis at the point $B$, then the incentre of the triangle $OAB$, where $O$ is the origin, is

Solution

Similar Questions

Let the equation of two sides of a triangle be $3x\,-\,2y\,+\,6\,=\,0$ and $4x\,+\,5y\,-\,20\,=\,0.$ If the orthocentre of this triangle is at $(1, 1),$ then the equation of its third side is

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