Question

1.4 homework question 23, 1.4.93 part 1 of 10 hw score: 84.62%, 22 of 26 points points: 0 of 1 either prove or disprove the statement, the points (-6, -4), (-2, -5), and (5,1) are the vertices of a right triangle. use a graph only as a guide. let the three points (-6, -4), (-2, -5), and (5,1) be labeled as a, b, and c respectively. graph the triangle formed by the vertices a, b, and c. choose the correct graph below.

Explanation:

To determine the correct graph, we analyze the coordinates of points \( A(-6, -4) \), \( B(-2, -5) \), and \( C(5, 1) \):

Step 1: Analyze \( x \)-coordinates

• \( A \) has \( x = -6 \) (leftmost), \( B \) has \( x = -2 \) (middle-left), \( C \) has \( x = 5 \) (rightmost).
• So \( A \) is left of \( B \), and \( B \) is left of \( C \).

Step 2: Analyze \( y \)-coordinates

• \( A \): \( y = -4 \); \( B \): \( y = -5 \) (so \( B \) is below \( A \)); \( C \): \( y = 1 \) (above both \( A \) and \( B \)).

Now, match to the graphs:

• Graph A: \( A \) is leftmost, \( B \) is below \( A \), \( C \) is rightmost and above. This matches the coordinate analysis.
• Other graphs (B, C, D) misalign with the \( x \)- or \( y \)-coordinate relationships (e.g., \( B \) not below \( A \), or \( C \) not rightmost).

Answer:

A. (The graph corresponding to option A, where \( A(-6, -4) \) is leftmost, \( B(-2, -5) \) is below \( A \), and \( C(5, 1) \) is rightmost and above.)