We appreciate your visit to KL is a segment representing one side of isosceles right triangle KLM with K 2 6 and L 4 2 KLM is a right angle. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the coordinates of vertex M for the isosceles right triangle KLM, where K(2, 6) and L(4, 2), you can follow these steps:
1. Find the Midpoint of KL:
The midpoint of a line segment connecting two points (x1, y1) and (x2, y2) is calculated as:
[tex]\[
\left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right)
\][/tex]
So, the midpoint of KL is:
[tex]\[
\left( \frac{2 + 4}{2}, \frac{6 + 2}{2} \right) = (3.0, 4.0)
\][/tex]
2. Calculate the Slope of KL:
The slope of a line passing through points (x1, y1) and (x2, y2) is:
[tex]\[
\text{slope} = \frac{y2 - y1}{x2 - x1}
\][/tex]
For KL:
[tex]\[
\text{slope} = \frac{2 - 6}{4 - 2} = \frac{-4}{2} = -2.0
\][/tex]
3. Determine the Perpendicular Slope:
In an isosceles right triangle, the legs are perpendicular. The perpendicular slope is the negative reciprocal of the original slope:
[tex]\[
\text{perpendicular slope} = -\frac{1}{\text{slope of KL}} = -\frac{1}{-2.0} = 0.5
\][/tex]
4. Find Possible Coordinates for M:
Since KL = LM and triangle KLM is isosceles, M must lie on the line that is perpendicular to KL and passes through the midpoint.
Using the perpendicular slope (0.5) and knowing the directions, you can find M as equidistant from K and L. Considering the perpendicular direction:
- Use some trigonometry to determine how you'd move from the midpoint to find the two potential points for M:
Taking into account the distance and direction, you have two possible coordinates for M:
- [tex]\( M_1 = (4.79, 4.89) \)[/tex]
- [tex]\( M_2 = (1.21, 3.11) \)[/tex]
These calculations let you find the possible coordinates for vertex M in the isosceles right triangle KLM given that KL = LM and the angle ZKLM is a right angle.
1. Find the Midpoint of KL:
The midpoint of a line segment connecting two points (x1, y1) and (x2, y2) is calculated as:
[tex]\[
\left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right)
\][/tex]
So, the midpoint of KL is:
[tex]\[
\left( \frac{2 + 4}{2}, \frac{6 + 2}{2} \right) = (3.0, 4.0)
\][/tex]
2. Calculate the Slope of KL:
The slope of a line passing through points (x1, y1) and (x2, y2) is:
[tex]\[
\text{slope} = \frac{y2 - y1}{x2 - x1}
\][/tex]
For KL:
[tex]\[
\text{slope} = \frac{2 - 6}{4 - 2} = \frac{-4}{2} = -2.0
\][/tex]
3. Determine the Perpendicular Slope:
In an isosceles right triangle, the legs are perpendicular. The perpendicular slope is the negative reciprocal of the original slope:
[tex]\[
\text{perpendicular slope} = -\frac{1}{\text{slope of KL}} = -\frac{1}{-2.0} = 0.5
\][/tex]
4. Find Possible Coordinates for M:
Since KL = LM and triangle KLM is isosceles, M must lie on the line that is perpendicular to KL and passes through the midpoint.
Using the perpendicular slope (0.5) and knowing the directions, you can find M as equidistant from K and L. Considering the perpendicular direction:
- Use some trigonometry to determine how you'd move from the midpoint to find the two potential points for M:
Taking into account the distance and direction, you have two possible coordinates for M:
- [tex]\( M_1 = (4.79, 4.89) \)[/tex]
- [tex]\( M_2 = (1.21, 3.11) \)[/tex]
These calculations let you find the possible coordinates for vertex M in the isosceles right triangle KLM given that KL = LM and the angle ZKLM is a right angle.
Thanks for taking the time to read KL is a segment representing one side of isosceles right triangle KLM with K 2 6 and L 4 2 KLM is a right angle. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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