Question

parallelogram efgh is shown below. give the coordinates of h.
g(-s,t) h(?,?)
f(0,0) e(u,0)

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite sides are equal and parallel. So, the vector from \( F \) to \( E \) should be the same as the vector from \( G \) to \( H \).
The coordinates of \( F \) are \( (0,0) \) and \( E \) are \( (u,0) \), so the vector \( \overrightarrow{FE} = (u - 0, 0 - 0)=(u,0) \).

Step2: Apply vector to find H

Let the coordinates of \( H \) be \( (x,y) \). The vector \( \overrightarrow{GH}=(x - (-s), y - t)=(x + s, y - t) \).
Since \( \overrightarrow{FE}=\overrightarrow{GH} \), we have \( x + s = u \) and \( y - t = 0 \).
Solving for \( x \) and \( y \): \( x = u - s \) and \( y = t \). So the coordinates of \( H \) are \( (u - s, t) \).

Answer:

\( (u - s, t) \)