Question

What is the x-coordinate of the point that divides the

Answer 1

There's a lot of information missing here, and the given list of choices is basically incomprehensible.

Suppose J (a, b) and K (c, d) are two points in the plane. We can trace out the line segment JK joining these points with the function

r(t) = (1 - t) (a, b) + t (c, d)

where 0 ≤ t ≤ 1.

Let P be the point that divides JK into line segments JP and PK having a length ratio of 2:5. Then JP is the point 2/7 of the way along JK, so that the coordinates of P are

P = r(2/7) = 5/7 (a, b) + 2/7 (c, d) = ((5a + 2c)/7, (5b + 2d)/7)

and in particular the x-coordinate of P is (5a + 2c)/7.