class 11

Math

Co-ordinate Geometry

Coordinate Geometry

If the line $2x+y=k$passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

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Figure shows the arrangement of desks in a classroom Ashima, Bharti and Camella are seated at A(3, 1), B(6, 4) and C(8, 6) respectively. Do you think they are seated in a line? Give reasons for your answer.

If A and B are $(2,2)and(2,4)$, respectively, find the coordinates of P such that $AP=73 AB$and P lies on the line segment AB.

Find the orthocentre of $ΔABC$ with vertices $A(1,0),B(−2,1),$ and $C(5,2)$

Find a relation between x and y such that the point (x, y) is equidistant from the point $(3,6)$ and $(3,4)$.

The distance between the circumcenter and the orthocentre of the triangle whose vertices are $(0,0),(6,8),$ and $(−4,3)$ is $L˙$ Then the value of $5 2 L$ is_________

If a triangle $ABC,A≡(1,10),$ circumcenter $≡(−31 ,32 ),$ and orthocentre $≡(411 ,34 )$ , then the coordinates of the midpoint of the side opposite to $A$ are $(1,−311 )$ (b) $(1,5)$ $(1,−3)$ (d) $(1,6)$

Find the area of the triangle whose vertices are (i) $(2,3),(–1,0),(2,–4)$ (ii) $(–5,–1),(3,–5),(5,2)$

Determine if the points $(1,5),(2,3)and(−2,−11)$ are collinear.