Yes, we can determine the other two vertices of the rectangle.

Given:

• Two vertices of the rectangle: $(-4, -3)$ and $(6, 5)$.
• The rectangle's sides are aligned with vertical and horizontal lines, which means the rectangle's sides are parallel to the x- and y-axes.

Steps to find the other two vertices:

1. Determine the x- and y-coordinates of the other vertices: Since the rectangle's sides are parallel to the axes, the other two vertices will share either the same x-coordinate or the same y-coordinate as one of the given vertices.

2. Vertices sharing the same x-coordinate:

   • The first given vertex is $(-4, -3)$, and the second is $(6, 5)$.
   • The x-coordinates of these two vertices are different, so the other two vertices will share either $-4$ or $6$ as their x-coordinate.

3. Find the other two vertices:

   • One vertex will have the x-coordinate $-4$ and the y-coordinate of the second vertex, $5$. This gives us the vertex $(-4, 5)$.
   • The other vertex will have the x-coordinate $6$ and the y-coordinate of the first vertex, $-3$. This gives us the vertex $(6, -3)$.

Conclusion:

The four vertices of the rectangle are:

• $(-4, -3)$ (given)
• $(6, 5)$ (given)
• $(-4, 5)$
• $(6, -3)$

Let me know if you need further clarification or have any questions!

5 Related Questions:

1. How do you identify the dimensions of the rectangle from its vertices?
2. What is the area of this rectangle?
3. How would you calculate the perimeter of this rectangle?
4. Can a rectangle have its sides not aligned with the coordinate axes? If so, how would the vertices be calculated?
5. How would you find the diagonal length of this rectangle?

Tip:

Always remember that when dealing with rectangles aligned with axes, the x- and y-coordinates of opposite vertices are either the same or different by the length of the sides. This property makes it easier to find missing vertices.