On a design plan for a landscaping project, a straight path runs from A(11, 29) to B(53, 9). A lamp is going to be placed halfway along the path. Determine the coordinates of the lamps location. Determine the length of the path.
I got 46.5 for the answer is that correct
That's what I get.
Thanks
To determine the coordinates of the lamp's location, we need to find the midpoint of the path between points A and B.
The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of points A and B.
The x-coordinate of the midpoint is (11 + 53) / 2 = 64 / 2 = 32.
The y-coordinate of the midpoint is (29 + 9) / 2 = 38 / 2 = 19.
Therefore, the coordinates of the lamp's location are (32, 19).
To determine the length of the path, 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)
Applying this formula to points A(11, 29) and B(53, 9), we get:
Distance = √((53 - 11)^2 + (9 - 29)^2)
= √(42^2 + (-20)^2)
= √(1764 + 400)
= √2164
≈ 46.5
So, your answer of 46.5 for the length of the path is correct.