what would the answer be if R(-4, -1) and T(3, 3) 

If the vertices \( R \) and \( T \) change to \( R(-4, -1) \) and \( T(3, 3) \), we need to recalculate the perimeter of quadrilateral RSTU with the updated points:

The new vertices are:

- \( R(-4, -1) \)
- \( S(-4, 4) \) (unchanged)
- \( T(3, 3) \)
- \( U(2, -2) \) (unchanged)

We'll again use the distance formula to find the updated distances between the adjacent vertices:

### 1. Distance \( RS \):
\[
RS = \sqrt{(-4 - (-4))^2 + (4 - (-1))^2} = \sqrt{0^2 + (5)^2} = \sqrt{25} = 5
\]

### 2. Distance \( ST \):
\[
ST = \sqrt{(3 - (-4))^2 + (3 - 4)^2} = \sqrt{(7)^2 + (-1)^2} = \sqrt{49 + 1} = \sqrt{50} = 5\sqrt{2}
\]

### 3. Distance \( TU \):
\[
TU = \sqrt{(2 - 3)^2 + (-2 - 3)^2} = \sqrt{(-1)^2 + (-5)^2} = \sqrt{1 + 25} = \sqrt{26}
\]

### 4. Distance \( UR \):
\[
UR = \sqrt{(-4 - 2)^2 + (-1 - (-2))^2} = \sqrt{(-6)^2 + (1)^2} = \sqrt{36 + 1} = \sqrt{37}
\]

### Calculating the Perimeter:
\[
\text{Perimeter} = RS + ST + TU + UR = 5 + 5\sqrt{2} + \sqrt{26} + \sqrt{37}
\]

Approximating the value:

\[
\approx 5 + 7.07 + 5.10 + 6.08 = 23.25
\]

So, the perimeter of quadrilateral RSTU with the updated vertices is approximately \( 23.25 \) units.

Would you like more details or have any other questions?

Here are 5 related questions:

1. How would the area of the quadrilateral change with the updated vertices?
2. What happens to the perimeter if \( S \) or \( U \) is moved?
3. How do changes in coordinates affect the symmetry of a quadrilateral?
4. Can you generalize how to find the perimeter for any shape using vertices?
5. How would you approach finding the centroid of quadrilateral RSTU?

**Tip:** When vertices change, recalculating each side’s length accurately is crucial for finding the correct perimeter or area of the shape.

Explore how to calculate the perimeter of quadrilateral RSTU with updated vertices R(-4, -1) and T(3, 3). This problem involves using the distance formula to find the lengths of sides RS, ST, TU, and UR, then summing them to determine the perimeter. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation