Question

Please help it due ASAP Please show workings

Answer 1

Answer:  Choice B

Point P is located at (-2, -1.8)

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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.

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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