Estefani's house is at point E (3, -2), and Jasmin's house is at point J (-5, 3). Jasmin's house is the midpoint between Estefani's and Preston's houses. What is the y-coordinate of Preston's house?
Mathematics · Middle School · Thu Feb 04 2021
Answered on
Since Jasmin's house is the midpoint between Estefani's and Preston's houses, we can use the midpoint formula to find the coordinates of Preston's house. The midpoint formula is given by:
Midpoint M(x,y) = ((x1 + x2)/2, (y1 + y2)/2)
Where (x1, y1) and (x2, y2) are the coordinates of the endpoints, and M(x,y) is the midpoint.
We know the coordinates of Estefani's house (E) are (3, -2) and Jasmin's midpoint (J) coordinates are (-5, 3). Let's denote the coordinates of Preston's house as (xp, yp).
Given J is the midpoint, we can set up the following equations:
(-5 + xp)/2 = 3 (for the x-coordinate) (3 + yp)/2 = -2 (for the y-coordinate)
Now, to find yp, solve the second equation:
(3 + yp)/2 = -2 Multiply both sides of the equation by 2 to isolate the yp term on one side: 3 + yp = -4 Subtract 3 from both sides: yp = -4 - 3 yp = -7
So, the y-coordinate of Preston's house is -7.
Extra: Understanding the midpoint formula is useful when you need to find a point that is exactly halfway between two other points on a coordinate plane. In two dimensions, the midpoint will have an x-coordinate that is the average of the two x-coordinates of the endpoints, and a y-coordinate that is the average of the two y-coordinates of the endpoints.
When you're given the midpoint and one endpoint and you need to find the other endpoint (as in this problem), you effectively reverse the formula. Instead of averaging the endpoints to find the midpoint, you use the midpoint to find the missing endpoint's coordinates. This involves setting up an equation where you know three of the four variables (the x-coordinate or the y-coordinate of midpoint, and the x and y-coordinates of one of the endpoints) and solving for the unknown. This can be particularly useful in various applications, including geometry, navigation, and even in computer graphics, where it's important to calculate points based on other reference points.