Parallelogram Coordinates Calculation
To find the coordinates of vertex S in parallelogram PQRS, we can use the property that opposite sides are parallel and equal in length, meaning the vectors representing opposite sides are equal.
Let the coordinates be P = $(-1, -1)$, Q = $(8, 0)$, R = $(7, 5)$, and S = $(x, y)$.
In a parallelogram PQRS, the vector $\vec{PQ}$ is equal to the vector $\vec{SR}$.
Vector Calculation
Calculate the vector $\vec{PQ}$:
$\vec{PQ} = Q - P = (8 - (-1), 0 - (-1)) = (8 + 1, 0 + 1) = (9, 1)$
Calculate the vector $\vec{SR}$:
$\vec{SR} = R - S = (7 - x, 5 - y)$
Equating Vectors
Since $\vec{PQ} = \vec{SR}$, we equate their components:
- For the x-component: $9 = 7 - x$
- For the y-component: $1 = 5 - y$
Solving for S Coordinates
Solve the equations:
From $9 = 7 - x$, we get $x = 7 - 9 = -2$.
From $1 = 5 - y$, we get $y = 5 - 1 = 4$.
Therefore, the coordinates of S are $(-2, 4)$.
Similar Questions
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Important Questions from Coordinate Geometry
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 16x + 38y + 425 = 0, then the value of x² + y² is:
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
- A geological survey team has established three research stations forming a triangular monitoring zone. The stations are located at coordinates P(2,5), Q(8,1), and R(4,9) on a coordinate grid where each unit represents 1 kilometer. What is the area of the triangular monitoring zone?
- \(A(1, 2)\), \(B(a, -26)\), \(C(13, -14)\) and \(D(6, 14)\) are the vertices of a parallelogram, taken in order, find the value of \(a\).
