Given the points J(-4,0) and K(0, 4), find the coordinates of the point P on directed line segment JK that partitions segment JK in the ratio 3:1

Step-by-step explanation:

We are given a ratio for this problem so we will use the formula for when we are given a ratio (as opposed to the formula for when you are given that the point you're looking for is a fraction of the way from one point to another, like 1/3 of the way from point A to point B. That's a different formula).

The formulas are for the x and y coordinates of the point in question:

  and   where

a = 3 (from the ratio),

b = 1 (from the ratio),

x1 = -4, y1 = 0 (from point J)

x2 = 0, y2 = 4 (from point K). Filling in for x first:

gives us

and now for y:

gives us

Therefore, the coordinates that partition that segment into the ratio of 3:1 are (-1, 3)

The measure of angle ∠DAB is 84

Step-by-step explanation:

Step 1:     96 + 96 = 192

Step 2:    360 - 192 = 168

Step 3:     168 / 2 = 84