Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202014 Oct 2020Evening ShiftMathematicsStraight LinesActual

If A(0,4,0), B(0,0,3) and C(0,4,3) are the vertices of A B C , then its incentre is

Options

  1. A(2,0,3)
  2. B(3,0,2)
  3. C(0,3,2)
  4. D(0,2,3)

Correct answer

C. (0,3,2)

Step-by-step solution

Let array ll a =4 j & | a |= a =4 b =3 k & | b |= b =3 c =4 j +3 k & | c |= c = 16+9 =5 array Let H( h ) be the incentre array l Incentre is given by a a +b b +c c a+b+c = h h = 4(4 j )+3(3 k )+5(4 j +3 k ) 4+3+5 = 16 j +9 k +20 j +15 k 12 = 36 j +24 k 12 =3 j +2 k array Thus co-ordinate of incentre is (0,3,2)

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are (1,2) and (4,5) , is 2025The coordinate axes are rotated about the origin in the counter clockwise direction through an angle 60^ . If a and b are the intercepts made on the new axes by a straight line who 2025The image of a point (2,-1) with respect to the line x-y+1=0 is 2025If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle 4 with the negative X -axis in the negative directi 2025A straight line passing through the origin O meets the parallel lines 4 x+2 y=9 and 2 x + y +6=0 at the points P and Q respectively. Then the point O divides the line segment PQ in 2025A (4,3), B (2,5) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoi 2025By shifting the origin to the point (2,3) through translation of axes, if the equation of the curve x^2+3 x y-2 y^2+4 x-y-20=0 is transformed to the form Ax ^2+ Bxy + Cy ^2+ Dx + E 2025The points (2,3) and (-4,- 4 3 ) lie on the opposite sides of the line L 5 x -6 y + k =0 and k is an integer. If the points (1,2) and (4,5) lie on the same side of the line L =0 , 2025 Full Straight Lines list All MHT CET PYQs