Question

click the arrows to choose an answer from each menu.
the fourth vertex is east of (-2, 3), so the choose... is the same as in point a. to find
the remaining coordinate, choose... .
aidan choose... .
the fourth vertex is located at choose... .

Explanation:

To solve this, we first identify the coordinates of the given points. Let's assume:

• Point \( A \) is \( (-2, 3) \) (top vertical point),
• Point \( B \) is \( (-2, -5) \) (bottom left),
• Point \( C \) is \( (1, -5) \) (bottom right).

Step 1: Analyze the "east of \((-2, 3)\)" clue

"East" means the \( x \)-coordinate increases (same direction as point \( C \) from \( B \), where \( x \) changes from \(-2\) to \( 1 \), so horizontal movement). The \( y \)-coordinate of the fourth vertex should match point \( A \) (since it’s east of \( A \), vertical position remains).

Step 2: Determine the \( x \)-coordinate

From \( B(-2, -5) \) to \( C(1, -5) \), the horizontal change is \( 1 - (-2) = 3 \). So, starting from \( A(-2, 3) \), add 3 to the \( x \)-coordinate:
\( x = -2 + 3 = 1 \).

Step 3: Determine the \( y \)-coordinate

The \( y \)-coordinate matches point \( A \), so \( y = 3 \).

Step 4: Locate the fourth vertex

The fourth vertex has coordinates \( (1, 3) \).

Filling the Menus:

1. "the [Choose...] is the same as in point \( A \)": This refers to the \( \boldsymbol{y\text{-coordinate}} \) (since east movement preserves \( y \)).
2. "To find the remaining coordinate, [Choose...]": Add the horizontal change (from \( B \) to \( C \)) to \( A \)’s \( x \)-coordinate (or calculate the horizontal shift).
3. "Aidan [Choose...]": (Assuming a context about plotting or calculating, but the key is the vertex.)
4. "The fourth vertex is located at [Choose...]": \( \boldsymbol{(1, 3)} \).

Answer:

• First "Choose": \( y\text{-coordinate} \)
• Second "Choose": Add the horizontal change (or similar)
• Third "Choose": (Depends on context, but the vertex is \( (1, 3) \))
• Fourth "Choose": \( (1, 3) \)