Question

P divides AB internally in the ratio 7 : 3. B is the point (10, 15) and P is (4, 6). Find the co-ordinates of A.

Answer 1

Answer:

ANSWER

Given, the point A divides the join of P(−5,1) and Q(3,5) in the ratio k:1.

By using section formula for internal division coordinates of A is,

A=(

k+1

3k−5

,

k+1

5k+1

) and B(1,5),C(7,−2)

So area of △ABC=

2

1

∣

∣

∣

∣

∣

k+1

3k−5

(5+2)+1(−2−

k+1

5k+1

)+7(

k+1

5k+1

−5)

∣

∣

∣

∣

∣

=2

⇒

2

1

∣

∣

∣

∣

∣

k+1

21k−35−2k−2−5k−1+35k+7−35k−35

∣

∣

∣

∣

∣

=2

⇒

∣

∣

∣

∣

∣

k+1

14k−66

∣

∣

∣

∣

∣

=4

taking the positive sign,

14k−66=4k+4

⇒10k=70

⇒k=7

taking the negative sign,

14k−66=−4k−4

⇒18k=62

⇒k=

9

31

hence,the value of k for the area of △ABC 2 sq units is 7,

9

31

.

Step-by-step explanation:

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