Question

coordinates (a,b) is the midpoint joining the points A(10,6) and B(k,4) and a -2b-18. find the value of k and distance AB

Answer 1

a(10,-6) ; b(k,4)


mid point=(X1+X2/2 , y1+y2/2)

(a,b)= (10+k/2 , -6+4/2)

= (10+k/2, -1)

a= (10+k/2)--------1

b=(-1)---------2

Now,
a -2 b=18 (sub 1 & 2 in this)

10+k/2 -2(-1)=18

10+k/2+2=18

10+k+4/2=18

k+14=18*2

k=36-14

k=22

ab=√(x1-x2)^2 + (y1-y2)^2

ab=√(10-22)^2 + (-6-4)^2

=√(-12)^2 + (-10)^2

√144+100= √244

Answer 2

please find the answer in the attachment.