Question

1. according to the diagram below, determine the lengths of $overline{bc}$ and $overline{bc}$ to determine if $overline{bc} cong overline{bc}$.

sides $overline{bc}$ and $overline{bc}$ are congruent and measure 2 units
sides $overline{bc}$ and $overline{bc}$ are congruent and measure 1 unit
sides $overline{bc}$ and $overline{bc}$ are not congruent. side $overline{bc}$ measures 1 unit, and side $overline{bc}$ measures 2 units
sides $overline{bc}$ and $overline{bc}$ are not congruent. side $overline{bc}$ measures 2 units, and side $overline{bc}$ measures 1 unit

Explanation:

To solve this, we analyze the coordinates (from the grid) of points \( B \), \( C \), \( B'' \), and \( C'' \):

Step 1: Determine length of \( \overline{BC} \)

• Assume \( B \) and \( C \) have vertical alignment (same \( x \)-coordinate). Count the vertical units between them. From the diagram, \( BC \) spans 2 units (e.g., if \( B \) is at \( (x, y_1) \) and \( C \) at \( (x, y_2) \), \( |y_1 - y_2| = 2 \)).

Step 2: Determine length of \( \overline{B''C''} \)

• Similarly, \( B'' \) and \( C'' \) are vertically aligned. Count the vertical units between them. From the diagram, \( B''C'' \) also spans 2 units (same logic as \( BC \)).

Step 3: Compare lengths

Since both \( \overline{BC} \) and \( \overline{B''C''} \) measure 2 units, they are congruent.

Answer:

A. Sides \( \overline{BC} \) and \( \overline{B''C''} \) are congruent and measure 2 units