Answer: Choice B
Point P is located at (-2, -1.8)
======================================================
Step-by-step explanation:
Refer to the diagram below. I've added point Q (2, -3) that is directly below point M, and directly to the right of point N. Right triangle MQN forms with the 90 degree angle at point Q.
The distance from N to Q is 5 units. Count the spaces or apply subtraction and absolute value to find this.
1/5 of this distance is (1/5)*5 = 1. Starting at point N, move 1 unit to the right to arrive at point A(-2,-3). Point P is directly above this point A, such that point P is on line segment MN.
In other words, point P has x coordinate x = -2. So the answer must be choice B as this is the only answer choice that has its point with x coordinate -2.
--------------------
The distance from Q to M is 6 units. Taking 1/5 of this leads to (1/5)*6 = 1.2
Start at point Q and move 1.2 units up to arrive at point B(2,-1.8). This point is on the same horizontal level as point P. So points B and P have the same y coordinate y = -1.8
The x coordinate of P is the same as the x coordinate of A(-2,-3)
The y coordinate of P is the same as the y coordinate of B(2,-1.8)
So overall, point P is located at P(-2,-1.8).
Again refer to the diagram. It shows point P directly above point A, and it shows point P on the same level as point B.
The length of segment NP is exactly 1/5 that of the length of segment NM.
We can write that as
NP = (1/5)*NM
this is equivalent to
5*NP = NM
after multiplying both sides by 5