Question

find the postive value of m for which the distance between teo points A(5,-3) and B(13,m) is 10 units

Answer 1

ratio=1:2

m1=1

M2=2

Y1=-3

Y2=m

M1×Y2+M2×Y1÷M1+M2

1×m+2×(-3)÷1+3=10

1m-6. =10

÷4. (cross multiplication)

40=1m-6

40+6=1m

《46=m》is the answer

Answer 2

Let A(5,-3)=A(x1,y1)

Let B(13,m)=B(x2,y2)

According to the distance formula,

d(A, B) =

$\sqrt{ {(x1 - y1}^{2} + {(x2 - y2)}^{2} } \: \: \\ \\ = \sqrt{ {( 5- 13) + ( - 3 - m)}^{2} } \\ \\ = \sqrt{ {( - 8)}^{2} + {( - 3)}^{2} - 2( - 3)(m) + {m}^{2}} \\ \\ = \sqrt{64 + 9 + 6m + {m}^{2} } \\ \\ = \sqrt{73 + 6m + {m}^{2} } \\ \\ = \sqrt{73} + \sqrt{6m} + m$

I couldn't find the answer maybe because the ratio wasn't given