On a site plan for a new house, a water main runs along the edge of the property straight from point W(10, 34) to point M(2, 2). The water service will enter the house at point H(24, 22). The grid intervals on the plan represent 0.5m.

Question

A) At what point on the water main should the connector to take water to the house be located? Explain your reason.
B) What length of the pipe will this require?

Answer 1

you have to draw a picture for this.
If I did it right, I would think you would want the water line to run in a straight line from MW.

To find the point on the water main,

step 1--I wrote the equation of the line from M to W, using the given points. Equation MW - y = 4x - 6

step 2.--I drew a straight line from MW to H. You need to find the point on MW, where the connector should be located.
Since the point @ H is (24, 22), the straight to MW will have 22 as the y-coordinate.

to find the x-coordinate on MW, substitute y = 22 in the equation
found in step 1, y = 4x - 6

The point I found was (7, 22), which will be where the connection for the water to the house will be located.

The reason I choose this location is because I would think that a water pipe should be run in a straight line to the house.

B. for the length of pipe, you need to find the distance from H (24, 22 ) to the connector (7, 22 ) on MW.

Using the distance formula,
d = (sqrt (x2 - x1)^2 + (y2 - y1)^2 )
d = 17

If each grid is 0.5m, 17 * .5 = 8.5 m

I leave this to you to follow the above logic, and draw this out and see if you come to the same conclusion as I did.

I am not a tutor