Question

find the value of x for whicj the distance between the points P(4,-5 ) and q(12,x) is 10​

Answer 1

Answer:

x=1,-11

Step-by-step explanation:

distance between two points PQ=10

coordinates of P(x1,y1)=(4,-5)

coordinates of Q(x2,y2)=(12,x)

so using distance formula :

d=sqrt[(x2-x1)²+(y2-y1)²]

10=sqrt[(12-4)²+(x-(-5))²]

10=sqrt[(8)²+(x+5)²]

10=sqrt[64+x²+25+10x] (opening the bracket (x+5)²

squaring both sides we get,

100=64+x²+25+10x

0=x²+10x+64+25-100

0=x²+10x-11

doing factors of the above eqjation we get :

0=x²-x+11x-11

0=x(x-1)+11(x-1)

0=(x+11)(x-1)

hence either x+11=0 or x-1=0

so we get two values of x which are x=1 , -11. Answer.....