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:-7Step-by-step explanation:The coordinates of the point wich divide the segment AB, where [tex]A(x_A,y_A),\ B(x_B,y_B)[/tex] in ratio [tex]m:n[/tex] can be calculated using formula[tex]C\left(\dfrac{nx_A+mx_B}{m+n},\dfrac{ny_A+my_B}{m+n}\right)[/tex]In your case,[tex]A(-4,-10)\\ \\B(-11,-7)\\ \\m:n=3:4\Rightarrow m=3,\ n=4[/tex]Hence,[tex]C\left(\dfrac{4\cdot (-4)+3\cdot (-11)}{3+4},\dfrac{4\cdot (-10)+3\cdot (-7)}{3+4}\right)\\ \\C\left(-\dfrac{49}{7},-\dfrac{61}{7}\right)\\ \\C\left(-7,-\dfrac{61}{7}\right)[/tex]Therefore, x-coordinate of the point that divides AB into a 3:4 ratio is -7.