How To Find The Endpoint In Geometry
Endpoint Formula
The endpoint formula is related to the midpoint formula. The signal in the eye/center of the line joining two points (also known every bit endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the midpoint formula. Allow united states of america explore the endpoint formula below.
What is Endpoint Formula?
The endpoint formula helps in determining the values of the endpoints in either a line segment or a ray. Endpoints are the endpoints of a line segment and one endpoint if it is a ray where both the line segment and the ray stop. The line does non extend whatsoever further from the endpoints. To summate the endpoints we need to know the midpoint formula. The midpoint is the heart or center point of any line that lies in the middle of the endpoints.
Let 1000 (\((x)_{g}\) , \((y)_{m}\)) exist a midpoint for the line joining two endpoints A (\((x)_{1}\) , \((y)_{1}\)) and B (\((x)_{2}\) , \((y)_{2}\)). We tin can use the midpoint formula to solve for either of the endpoints. Given the coordinates of Grand and A, the coordinates of B can be calculated using the following formula:
(From the midpoint formula)
\((x)_{m}\)= \( \dfrac{x_1 + x_2}{2} \),
\((y)_{m}\) = \( \dfrac{y_1 + y_2}{ii} \)
\((x)_{two}\) = 2\((x)_{g}\)- \((x)_{one}\),
\((y)_{ii}\) = 2\((y)_{grand}\)- \((y)_{1}\)
Thus, the endpoint formula is,
Endpoint formula of B(\((x)_{2}\), \((y)_{2}\)) = (two\((x)_{k}\)- \((x)_{1}\), 2\((y)_{m}\)- \((y)_{1}\))
Annotation: It is non recommended to learn this formula, rather but find the coordinates of B by just using the midpoint formula.
Endpoint Formula
By solving the midpoint formula for the points x2 and ytwo, we get the endpoint formula, i.e.
Endpoint formula of B(\((ten)_{two}\), \((y)_{2}\)) = (two\((x)_{m}\)- \((x)_{1}\), 2\((y)_{yard}\)- \((y)_{1}\))
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Examples Using Endpoint Formula
Case 1: M(iii, 4) is the midpoint of the line joining points A(5, two) and B(x, y). Find the coordinates of B using the endpoint formula.
Solution:
Given,
\((10)_{m}\) = three, \((x)_{1}\) = 5, \((y)_{m}\) = iv, \((y)_{1}\) = 2
Using the endpoint formula,
\((x)_{2}\) = two\((x)_{thou}\)- \((10)_{1}\)
\((10)_{two}\) = 2 × 3 - 5
\((10)_{two}\) = 1
\((y)_{2}\) = 2\((y)_{m}\)- \((y)_{i}\)
\((y)_{two}\) = 2 × iv - 2
\((y)_{ii}\) = half-dozen
x = 1, y = half-dozen
Therefore, the coordinates of B(ten, y) = (1, 6), i.due east. 10 = ane and y = half-dozen
Example 2: C (seven, viii) is the centre of the circle having a radius = 5 units. A diameter is drawn on this circle, and one of its endpoints is (3, 5). Notice the other endpoint of the bore using the endpoint formula.
Solution:
Let E(x, y) be the other endpoint and C is the midpoint of a diameter. Given,
\((x)_{1000}\) = 7, \((10)_{one}\) = 3, \((y)_{m}\) = 8, \((y)_{ane}\) = v
Using the endpoint formula,
\((x)_{ii}\) = ii\((ten)_{k}\)- \((ten)_{1}\)
\((x)_{2}\) = ii × 7 - 3
\((x)_{2}\) = 11
\((y)_{2}\) = two\((y)_{m}\)- \((y)_{1}\)
\((y)_{2}\) = two × 8 - 5
\((y)_{2}\) = 11
ten = 11, y = 11
Therefore, the coordinates of the other endpoint Eastward(x, y) is (11, 11)
Example 3: P(five, eight) is the midpoint of the line joining points A(4, 3) and B(x, y). Notice the coordinates of B using the endpoint formula.
Solution:
Given,
\((x)_{m}\) = v , \((x)_{one}\) = 4, \((y)_{m}\) = 8, \((y)_{one}\) = 3
Using the Endpoint Formula,
\((x)_{2}\) = 2\((ten)_{one thousand}\)- \((x)_{one}\)
\((x)_{2}\) = 2 × 5 - 4
\((x)_{two}\) = half-dozen
\((y)_{2}\) = 2\((y)_{m}\)- \((y)_{1}\)
\((y)_{2}\) = 2 × 8 - 3
\((y)_{2}\) = 13
x = vi, y = thirteen
Therefore, the coordinates of B(x, y) = (vi, 13), i.e. x = 6 and y = xiii
FAQs on Endpoint Formula
What is Meant by Endpoint Formula?
The endpoint formula is related to the midpoint formula. The point in the middle/center of the line joining two points (too known as endpoints) is called a midpoint. Given ane endpoint and a midpoint, the other midpoint tin can be calculated using the midpoint formula. The endpoint formula of B(\((x)_{2}\), \((y)_{ii}\)) = (2\((x)_{m}\)- \((10)_{ane}\), 2\((y)_{thou}\)- \((y)_{1}\))
What is the Formula to Calculate the Endpoint?
Permit M (\((ten)_{thousand}\) , \((y)_{m}\)) be a midpoint for the line joining ii endpoints A (\((x)_{one}\) , \((y)_{1}\)) and B (\((x)_{2}\) , \((y)_{2}\)). We can apply the midpoint formula to solve for either of the endpoints. Given the coordinates of M and A, the coordinates of B can exist calculated using the following formula:
(From the midpoint formula)
\((x)_{m}\)= \( \dfrac{x_1 + x_2}{2} \),
\((y)_{chiliad}\) = \( \dfrac{y_1 + y_2}{2} \)
\((x)_{two}\) = two\((x)_{thousand}\)- \((x)_{i}\),
\((y)_{2}\) = 2\((y)_{m}\)- \((y)_{1}\)
Thus, the endpoint formula is,
Endpoint formula of B(\((x)_{two}\), \((y)_{ii}\)) = (2\((x)_{grand}\)- \((x)_{1}\), 2\((y)_{m}\)- \((y)_{ane}\))
What is the Midpoint Formula for Calculating the Endpoints?
The endpoints can be calculated past using the midpoint formula:
(From the midpoint formula)
\((x)_{1000}\)= \( \dfrac{x_1 + x_2}{2} \),
\((y)_{thousand}\) = \( \dfrac{y_1 + y_2}{2} \)
\((10)_{2}\) = 2\((x)_{yard}\)- \((ten)_{1}\),
\((y)_{2}\) = 2\((y)_{m}\)- \((y)_{1}\)
Using the Endpoint Formula, Calculate the Coordinates of B with Southward(ten, 7) existence the Midpoint of the Line Joining Points A(7, iv) and B(x, y).
Given,
\((x)_{m}\) = 10, \((x)_{i}\) = 7, \((y)_{m}\) = 7, \((y)_{1}\) = iv
Using the endpoint formula,
\((ten)_{2}\) = 2\((x)_{thousand}\)- \((x)_{i}\)
\((ten)_{ii}\) = 2 × 10 - 7
\((x)_{2}\) = 13
\((y)_{ii}\) = 2\((y)_{m}\)- \((y)_{1}\)
\((y)_{2}\) = ii × seven - 4
\((y)_{two}\) = 10
x = 13, y = 10
Therefore, the coordinates of B(x, y) = (thirteen, 10), i.e. ten = 13 and y = 10
Source: https://www.cuemath.com/endpoint-formula/
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