CBSE Guess > Papers > Question Papers > Class X > 2009 > Mathematics > Mathematics

Q. 21. Point P, Q, R and S in that order are dividing a line segment joining A(2, 6) and B(7, – 4) in five equal parts. Find the coordinates of P and R.

AP : PB = 1 : 4

P

=
AR:RB=3:2

R
=

Q. 22. A (– 4, – 2), B(– 3, – 5), C(3, – 2) and D(2, k) are the vertices of a quadrilateral ABCD. Find the value of k, if the area of the quadrilateral is 28 sq. units.

Sol.

ar(ABC)

= + (-3)[ -2 – (-2 )] + 3[ -2-(-5)] (-4 , -2)

= -3 (-2+2 + 3 (-2 + 5) ]

=-3(0) + 3 (3 ) ]

=

ar ( ABC)ar( ABD) =28

+ ar (ACD)= 28

ar ( ACD) =28 - = =

[-4(-2-k) + 3 (k- (-2)) + 2(-2-(-2))] =

8 + 4k + 3k + 6 = 35

7k + 14 = 35

k + 2 = 5 …(Dividing both sides by 7)

k = 5 – 2

k = 5 – 2 or k = – 5 – 2

k = 3 or k = – 7

Mathematics 2009 Question Papers Class X
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