Question

Identify the correct set up for finding the distance between points U(-3, 6) and V(5, 7).

Answer 1

What is the area of the given triangle?


1 point
Captionless Image
120 sq meters
60 sq meters
96 sq meters
22 sq meters

Answer 2

To find the distance between two points \( U(-3, 6) \) and \( V(5, 7) \) in a Cartesian coordinate system, you can use the distance formula, which is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \( (x_1, y_1) \) corresponds to the coordinates of point U, and \( (x_2, y_2) \) corresponds to the coordinates of point V.

1. Identify the coordinates:
- For point U: \( x_1 = -3 \), \( y_1 = 6 \)
- For point V: \( x_2 = 5 \), \( y_2 = 7 \)

2. Substitute the coordinates into the distance formula:
\[
d = \sqrt{(5 - (-3))^2 + (7 - 6)^2}
\]

3. Simplify the expression:
\[
d = \sqrt{(5 + 3)^2 + (1)^2}
\]
\[
d = \sqrt{(8)^2 + (1)^2}
\]
\[
d = \sqrt{64 + 1}
\]
\[
d = \sqrt{65}
\]

Thus, the correct setup for finding the distance between the points U and V is:

\[
d = \sqrt{(5 - (-3))^2 + (7 - 6)^2}
\]

and the calculated distance is \( d = \sqrt{65} \).

Answer 3

To calculate the area of a triangle, you can use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

However, since you mentioned "the given triangle" but did not provide any dimensions, I can't directly calculate the area without knowing the base and height of the triangle or any other relevant measurements (like the lengths of the sides).

If you can provide either the dimensions of the triangle or a description of its vertices, I would be happy to help you find the area! Alternatively, if this is a multiple-choice question, please let me know if there are any additional options or information about the triangle that can assist in determining the correct area.