Question

Given the vertices A(−3,4)
, B(8,4)
, and C(8,−7)
, which of the following is the final point needed to construct a square? (1 point)
Responses

(8,−7)
left parenthesis 8 comma negative 7 right parenthesis

(8,4)
left parenthesis 8 comma 4 right parenthesis

(−3,4)
left parenthesis negative 3 comma 4 right parenthesis

(−3,−7)

Answer 1

To determine the fourth vertex needed to construct a square with the given vertices \( A(-3, 4) \), \( B(8, 4) \), and \( C(8, -7) \), we first analyze the positions of the existing points:

- Points A and B are horizontally aligned since they share the same y-coordinate (y = 4).
- Point C is vertically aligned with point B since they share the same x-coordinate (x = 8).

Given these points, we can picture the square:

1. **Point A**: \( (-3, 4) \) (top left)
2. **Point B**: \( (8, 4) \) (top right)
3. **Point C**: \( (8, -7) \) (bottom right)

To form a square, the fourth vertex \( D \) (which we need to find) must be directly below point \( A \) by the same distance that point \( C \) is below point \( B \).

The distance between \( A \) and \( B \) horizontally is:
\[
8 - (-3) = 11
\]
The vertical distance from \( B \) to \( C \) is:
\[
4 - (-7) = 11
\]

Thus, to find point \( D \), which is below \( A \), we move down from \( A \) by 11 units:
\[
D = (-3, 4 - 11) = (-3, -7)
\]

Now, let's check the given responses to find the correct fourth vertex:
- (8, -7)
- (8, 4)
- (-3, 4)
- (-3, -7)

The correct point to complete the square is \( (-3, -7) \).

**Final Answer: \( (-3, -7) \)**