(a) find the lengths of the sides of R S T,(b) use the converse of the Pythagorean Theorem to sh

Name: Problem 29, Chapter 13: Geometry
Uploaded: 2019-10-08T22:40:48-08:00
Duration: 1 min 13 s
Channel: Amrita Bhasin
Description: (a) find the lengths of the sides of R S T,(b) use the converse of the Pythagorean Theorem to show that R S T is a right triangle, and (c) find the product of the slopes of R T and S T. R(4,3), S(-3,6), T(2,1)

step 1 Okay, for RS, if we're plugging into the distance formula, we have the square root of 4 plus 3 s

Question

(a) find the lengths of the sides of $\triangle R S T,(b)$ use the converse of the Pythagorean Theorem to show that $\triangle R S T$ is a right triangle, and (c) find the product of the slopes of $\overline{R T}$ and $\overline{S T}$. $R(4,3), S(-3,6), T(2,1)$

   (a) find the lengths of the sides of $\triangle R S T,(b)$ use the converse of the Pythagorean Theorem to show that $\triangle R S T$ is a right triangle, and (c) find the product of the slopes of $\overline{R T}$ and $\overline{S T}$.

$R(4,3), S(-3,6), T(2,1)$

Geometry

Ray C.… 1st Edition

Chapter 13, Problem 29

Instant Answer

Solved by Expert Amrita Bhasin

10/08/2019

Step 1

We can use the distance formula to do this. The distance formula is given by $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. For $RS$, we have $d=\sqrt{(4-(-3))^2+(3-6)^2}=\sqrt{49+9}=\sqrt{58}$. For $ST$, we have $d=\sqrt{(-3-2)^2+(6-1)^2}=\sqrt{25+25}=\sqrt{50}$. For Show more…

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(a) find the lengths of the sides of $\triangle R S T,(b)$ use the converse of the Pythagorean Theorem to show that $\triangle R S T$ is a right triangle, and (c) find the product of the slopes of $\overline{R T}$ and $\overline{S T}$. $R(4,3), S(-3,6), T(2,1)$

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Key Concepts

Distance Formula

The Distance Formula is used to calculate the length of a segment between two points in a coordinate plane. It is derived from the Pythagorean Theorem and is essential for determining distances between vertices of geometric figures such as triangles.

Converse of the Pythagorean Theorem

The Converse of the Pythagorean Theorem is used to determine whether a triangle is a right triangle. It states that if the sum of the squares of two sides equals the square of the third side, then the triangle is right-angled.

Slope Formula and Perpendicular Slopes

The Slope Formula calculates the rate of change between two points on a line and is crucial in coordinate geometry. Additionally, when the slopes of two lines are negative reciprocals of each other (i.e., their product is -1), the lines are perpendicular, indicating a right angle between them.

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