Question

For what values of p and q will the following pair of linear equations has infinitely many solution? 4x+5y=2;(2p+7p)x+(p+8q)y=2q-p+1

Answer 1

let the points be A(a,b), B(c,d) and C(e,f) respectively. let  P(10,5),Q(8,4) and R(6,6) be the mid points of AB, BC and AC respectively.

since P(10,5) is the mid point of AB

therefore  a +c  =  10*2=20................(1)

and  b + d = 10......................(2)

Q(8,4) is the mid point of BC

so, c + e =16......................(3)

and  d + f =8 ....................(4)

 

and R(6,6) is the mid point of AC 

a + e =12......................(5)

 b + f = 12................(6)

on solving (1) (3) and (5) We get

a= 8, c=12,e=4 and similarly on solving (2) (4) and (6) we get

b=7,f=5 and d =3

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Varshakutty96... asked in Math

if(-4,3)and(4,3)are two vertices of an equilateral triangle. find the coordinates of the third vertex. given that the origin lies in the interior of the triangle.

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Ankush Jain answered this
11035 helpful votes in Math, Class XII-Science

Let the co-ordinate of third vertex be (x, y)



Now Using Distance formula





Given, ΔABC is equilateral triangle

∴ AB = AC = BC

Now, AB = AC



On Squaring both sides, we get

(x + 4)2 + (y – 3)2 = (x – 4)2 + (y – 3)2

(x + 4)2 = (x – 4)2

or x2 + 16 + 8x = x2 + 16 – 8x

⇒ 16x = 0

x = 0  ....(1)

AC = BC implies that



On squaring both sides, we get

16 + y2 + 9 – 6y = 64

y2 – 6y – 39 = 0



, as origin lies in the interior of the triangle

Third vertex

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