The points P(-2, 1), Q(-6, 4) and R(4,3) are three verticies of parallelogram PQRS .
Find the coordinate S.
An easy way to do this would be to graph the points. There are actually two answers: one for the case in which Q and R are at opposite corners, and another for the case in which QR is a side of the parallelogram. I assume they want the latter. In that case, S is (8,0). Just make the changes in x and y when going from R to S the same as the changes going from Q to P.
To find the coordinate of point S, we need to determine the relationship between the coordinates of the given points P, Q, and R in the parallelogram PQRS.
A parallelogram has opposite sides that are parallel and equal length. Therefore, the vector formed by the coordinates of P and Q should be equal to the vector formed by the coordinates of R and S.
Let's find the vector formed by the coordinates of P and Q:
Vector PQ = Q - P = (-6, 4) - (-2, 1) = (-6 + 2, 4 - 1) = (-8, 3).
Now, since the opposite sides of a parallelogram are parallel, the vector formed by the coordinates of R and S should also be equal to (-8, 3).
Let's set up the equation:
Vector RS = S - R = (-8, 3).
To find S, we rearrange the equation:
S = Vector RS + R.
Substituting the values of R = (4, 3) and Vector RS = (-8, 3) into the equation, we get:
S = (-8, 3) + (4, 3)
= (-8 + 4, 3 + 3)
= (-4, 6).
Therefore, the coordinate of point S in the parallelogram PQRS is S(-4, 6).
To find the coordinates of point S, we need to use the property of parallelograms that opposite sides are parallel and equal in length.
Step 1: Find the vector between points P and Q.
Vector PQ = (x2 - x1, y2 - y1)
Vector PQ = (-6 - (-2), 4 - 1)
Vector PQ = (-4, 3)
Step 2: Find the vector from point R to the point Q.
Vector QR = (x2 - x1, y2 - y1)
Vector QR = (-6 - 4, 4 - 3)
Vector QR = (-10, 1)
Step 3: Add vector QR to point P to find the coordinates of point S.
S = P + QR
S = (-2, 1) + (-10, 1)
S = (-2 - 10, 1 + 1)
S = (-12, 2)
Therefore, the coordinate of point S is (-12, 2).