Explanation:
this is similar to the general midpoint calculation. just instead of 1/2 we are looking for 7/10 of the distance.
in principle we are looking for
A + (B - A)×7/10
(-4, -7) + ((11 - -4)×7/10, (5 - -7)×7/10) =
= (-4, -7) + (15×7/10, 12×7/10) =
= (-4, -7) + (10.5, 8,4) = (6.5, 1.4)
so, the point 7/10 of the way from A to B is
(6.5, 1.4).
a quick check :
the distance from A to B :
distanceAB² = (11 - -4)² + (5 - -7)² = 15² + 12² =
= 225 + 144 = 369
distanceAB = 19.20937271...
7/10 of distanceAB = 7/10×19.20937271... =
= 13.4465609...
the distance from A to point 7/10 :
distanceA7/10² = 10.5² + 8.4² = 110.25 + 70.56 =
= 180.81
distance A7/10 = 13.4465609...
that is identical to 7/10 of the distance between A and B.
so, our approach is correct.
(6.5, 1.4) is the correct point.