The points P(-2, 1), Q(-6, 4) and R(4,3) are three verticies of parallelogram PQRS .
Find the coordinate S.
let S(a,b) be the other point
vector PS = vector QR
[a+2,b-1] = [10,-1]
a+2=10 ---> a = 8
b-1=-1 ---> b = 0
S is (8,0)
Check by finding slope of SR and PQ, it works
To find the coordinates of point S, we need to understand the properties of a parallelogram.
In a parallelogram, opposite sides are equal in length and parallel to each other. This means that if we find the midpoint of diagonal QR, we can use it to calculate the coordinates of point S.
1. Find the mid-point of QR:
The coordinates of Q and R are (-6, 4) and (4, 3) respectively.
To find the midpoint, we can use the midpoint formula:
Midpoint (M) = [(x1 + x2)/2, (y1 + y2)/2]
Substituting the coordinates of Q and R:
M = [(-6 + 4)/2, (4 + 3)/2]
= [-1, 7/2]
= (-1, 3.5)
2. Using the midpoint, we can find point S:
Since S and M are midpoints of their respective diagonals, they divide each other in equal parts.
The coordinates of point P are (-2, 1).
To find point S, we can use the relation between diagonals of a parallelogram:
S = 2M - P
Substituting the coordinates of M and P:
S = [2(-1) - (-2), 2(3.5) - 1]
= [-2 + 2, 7 - 1]
= [0, 6]
= (0, 6)
Therefore, the coordinates of point S are (0, 6).