Line segment ab has endpoints a(7, 4) and b(2, 5). find the coordinates of the point that divides the line segment directed from a to b in the ratio of 1: 3.

Step-by-step explanation:

We have been given that line segment AB has endpoints A(7, 4) and B(2, 5). We are asked to find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.

To solve our given problem we will use section formula.

Section formula states, when a point P divides a line segment AB internally in ratio m:n, so the coordinates of point P are:

Let , , .

Upon substituting coordinates of our given points in section formula we will get,

Therefore, the coordinates of point that divides the line segment AB in the ratio 1:3 are .

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.