What is the orthocenter of a triangle with corners at #(4 ,3 )#, #(7 ,4 )#, and (2 ,8 )#?

Answer 1

The Orthocentre is #(64/17,46/17).#

Let us name the corners of the triangle as #A(4,3), B(7,4) & C(2,8).#

From Geometry , we know that the altitudes of a trangle are concurrent at a point called the Orthocentre of the triangle.

Let pt. #H# be the orthocentre of #DeltaABC,# and, let three altds. be #AD, BE, and CF,# where the pts. #D,E,F# are the feet of these altds. on sides #BC, CA, and, AB,# respectively.
So, to obtain #H#, we should find the eqns. of any two altds. and solve them. We select to find the eqns. of #AD and CF.#

Eqn. of Altd. AD :-

#AD# is perp. to #BC#, & slope of #BC# is #(8-4)/(2-7)=-4/5,# so, slope of #AD# has to be #5/4#, with #A(4,3)# on #AD#.
Hence, eqn. of #AD : y-3=5/4(x-4),# i.e., #y=3+5/4(x-4)..........(1)#

Eqn. of Altd. CF :-

Proceeding as above, we get , eqn. of #CF : y=8-3(x-2)........(2)#
Solving #(1) & (2), 3+5/4(x-4)=8-3(x-2)# #rArr 12+5x-20=32-12x+24 rArr 17x=64 rArr x=64/17# BY #(2)#, then, #y=8-3*30/17=46/17.#
Hence, the Ortho centre #H=H(64/17,46/17).#

Hope, you enjoyed this! Enjoy Maths.!

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Answer 2

The orthocenter of the triangle with corners at (4, 3), (7, 4), and (2, 8) is approximately (5.06, 6.89).

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Answer 3

The orthocenter of a triangle is the point where all the altitudes of the triangle intersect. To find the orthocenter of the triangle with vertices at (4, 3), (7, 4), and (2, 8), you would need to find the intersection point of the altitudes.

The altitudes of a triangle are perpendicular lines drawn from each vertex to the opposite side. You can find the equations of these lines and then solve for their intersection point.

Once you have the equations of the altitudes and their intersection point, you will have found the orthocenter of the triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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