Line segment ab has endpoints a(1, 2) and b(5, 3). find the coordinates of the point that divides the line segment directed from a to b in the ratio of 1: 3. a) (4, 2) b) (3, 5/2) c) (2/3, 2) d) (2, 9/4)

Now despite what you may think, 1:3 is not 1/3 in this situation, but rather it's "1 equal part to 3 equal parts", which is a total of 4 equal parts. In short, they want the point that is at the 1/4 mark from A to B.

Firstly, how many units apart is 1 to 5 (the x-coordinates)? That would be 4 units apart. Multiply 1/4 by 4:

Next, how many units apart is 2 to 3 (the y-coordinates)? That would be 1 unit apart. Multiply 1/4 by 1:

Next, since from 1 to 5 you are increasing, add 1 to 1.

2 is the x-coordinate of the new point.

Next, since from 2 to 3 you are increasing, add 1/4 to 2.

9/4 is the y-coordinate of the new point.

Putting it together, the point which divides AB into a 1:3 ratio is (2, 9/4), or D.

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b