Question

16. PORS is a square where P = ( -3,4 )Q = (0,7) and R=(- 3. 10). Find the co-ordinates of S.​

Answer 1

Answer:

Step-by-step explanation:

PQRS is a square, the length of the sides of the square are equal, i,e. Length of PQ, QR, RS, SP are equal

Now the co-ordinate of P is (-3, 4)

Co-ordinate of Q is (0, 7)

Co-ordinate of R is (-3, 10)

Now we have to find the co-ordinate of S

Distance between P and Q is =√((-3-0) ^2+(4-7) ^2) = √((-3) ^2+(-3) ^2) =√(9+9) =√18 units

So length of PQ is =√18 units= length of QR = length of RS = length of SP

Now now let co-ordinate of S is (x, y) then

SP^2 = 18 | RS^2=18

=>(x+3) ^2+(y-4) ^2=18|=>(x+3) ^2+(y-10) ^2=18

=>(x+3) ^2=18-(y-4) ^2

Now we get from the second equation by putting the value of (x+3) ^2,

18-(y-4) ^2+(y-10) ^2=18

This implies, (y-4) ^2 = (y-10) ^2

=>y^2-8y+16=y^3-20y+100

=>12y=84 => y=7

So, (x+3) ^2=18-(7-4) ^2=18-9=9

So, (x+3) = 3=>x =0

So the co-ordinate of S is (0, 7)