Find the lengths of the sides of the triangle PQR. P(1, 2, 4), Q(3, 4, 3), R(3, -2, 0) |PQ| = |QR| = |RP| = Is it a right triangle? Yes Ο No Is it an isosceles triangle? Yes O No Need Help? Read It Viewing Saved Work Revert to Last Response
Find the lengths of the sides of the triangle PQR. P(1, 2, 4), Q(3, 4, 3), R(3, -2, 0) |PQ| = |QR| = |RP| = Is it a right triangle? Yes Ο No Is it an isosceles triangle? Yes O No Need Help? Read It Viewing Saved Work Revert to Last Response
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Find the Lengths of the Sides of the Triangle PQR**
Given the points:
- \( P (1, 2, 4) \)
- \( Q (3, 4, 3) \)
- \( R (3, -2, 0) \)
Calculate the lengths of the sides \( \overline{PQ} \), \( \overline{QR} \), and \( \overline{RP} \) using the distance formula in 3D space:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
**Distance PQ:**
\[ |PQ| = \]
**Distance QR:**
\[ |QR| = \]
**Distance RP:**
\[ |RP| = \]
**Determine Triangle Properties:**
Is it a right triangle?
- \( \circ \) Yes
- \( \circ \) No
Is it an isoscele triangle?
- \( \circ \) Yes
- \( \circ \) No
[Need Help?](#)
*You can find additional information and step-by-step guides by clicking the "Read It" button.*
**Note:** The calculations should follow the applicable mathematical methods for finding distances in 3D space to determine the sides and check for right angle or isosceles properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf9eba19-7b67-4fcd-8970-a14a27c2cd15%2F57272f99-62a5-4376-a769-fbe67a08e06a%2Fsl537db_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Lengths of the Sides of the Triangle PQR**
Given the points:
- \( P (1, 2, 4) \)
- \( Q (3, 4, 3) \)
- \( R (3, -2, 0) \)
Calculate the lengths of the sides \( \overline{PQ} \), \( \overline{QR} \), and \( \overline{RP} \) using the distance formula in 3D space:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
**Distance PQ:**
\[ |PQ| = \]
**Distance QR:**
\[ |QR| = \]
**Distance RP:**
\[ |RP| = \]
**Determine Triangle Properties:**
Is it a right triangle?
- \( \circ \) Yes
- \( \circ \) No
Is it an isoscele triangle?
- \( \circ \) Yes
- \( \circ \) No
[Need Help?](#)
*You can find additional information and step-by-step guides by clicking the "Read It" button.*
**Note:** The calculations should follow the applicable mathematical methods for finding distances in 3D space to determine the sides and check for right angle or isosceles properties.
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