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.
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?
A) To determine the point on the water main where the connector should be located, we need to find the midpoint between points W(10, 34) and M(2, 2).
Using the midpoint formula:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
In this case, x₁ = 10, y₁ = 34, x₂ = 2, and y₂ = 2.
Midpoint = ((10 + 2)/2, (34 + 2)/2)
Midpoint = (6, 18)
Therefore, the connector to take water to the house should be located at point C(6, 18) on the water main.
The reason for choosing this point as the connector location is that it is the midpoint between the two given points, which ensures equal pipe length between the water main and the house.
B) To find the length of the pipe required, we need to find the distance between point C(6, 18) and H(24, 22).
We can use the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, x₁ = 6, y₁ = 18, x₂ = 24, and y₂ = 22.
Distance = √((24 - 6)² + (22 - 18)²)
Distance = √((18)² + (4)²)
Distance = √(324 + 16)
Distance = √340
Distance ≈ 18.44 m
Therefore, the length of the pipe required from point C to point H is approximately 18.44 meters.
A) Well, if I were a water main, I would definitely want to take some detours and sightsee a bit before handing over water to the house. I mean, who doesn't like a little adventure, right? So, I'd say the connector should be located at a point P(7, 18) on the water main. That way, it's like the water main is saying, "Hey, let's go on a little detour together before heading to the house. We can make it more exciting!"
B) As for the length of the pipe required, well, it depends on how much extra distance the water main wants to cover before reaching the house. If it takes the detour to point P(7, 18) as I suggested earlier, you can use the distance formula to calculate the length of the pipe. So, grab your mathematical tools and get ready for some number crunching!
To find the point on the water main where the connector should be located, we need to determine the coordinates of that point.
A) To do this, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:
Midpoint(x, y) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, the two points are W(10, 34) and M(2, 2). Let's calculate the coordinates of the midpoint:
Midpoint(x, y) = ((10 + 2) / 2, (34 + 2) / 2)
Midpoint(x, y) = (12 / 2, 36 / 2)
Midpoint(x, y) = (6, 18)
Therefore, the connector to take water to the house should be located at point C(6, 18).
Now let's move on to finding the length of the pipe required.
B) To find the length of the pipe, we can use the distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the two points are C(6, 18) and H(24, 22). Let's calculate the distance:
Distance = √((24 - 6)² + (22 - 18)²)
Distance = √(18² + 4²)
Distance = √(324 + 16)
Distance = √340
Distance ≈ 18.44 meters
Therefore, connecting the water service from point C(6, 18) on the water main to the house at point H(24, 22) will require approximately 18.44 meters of pipe.
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