Question

Ine segment AB has endpoints A(–4, –10) and B(–11, –7). To find the x-coordinate of the point that divides the directed line segment in a 3:4 ratio, the formula x = (x2 – x1) + x1 was used to find that x = (–11 – (–4)) + (–4).

Therefore, the x-coordinate of the point that divides AB into a 3:4 ratio is

Answer 1

-7

Explanation:

The coordinates of the point wich divide the segment AB, where
`A(x_A,y_A),\ B(x_B,y_B)` in ratio
`m:n` can be calculated using formula

`C\left((nx_A+mx_B)/(m+n),(ny_A+my_B)/(m+n)\right)`

In your case,

`A(-4,-10)\\ \\B(-11,-7)\\ \\m:n=3:4\Rightarrow m=3,\ n=4`

Hence,

`C\left((4\cdot (-4)+3\cdot (-11))/(3+4),(4\cdot (-10)+3\cdot (-7))/(3+4)\right)\\ \\C\left(-(49)/(7),-(61)/(7)\right)\\ \\C\left(-7,-(61)/(7)\right)`

Therefore, x-coordinate of the point that divides AB into a 3:4 ratio is -7.