A triangle has corners A, B, and C located at #(1 ,3 )#, #(9 ,5 )#, and #(6 ,2 )#, respectively. What are the endpoints and length of the altitude going through corner C?

Answer 1

The endpoints are #(93/17, 70/17)#

length#=(9sqrt17)/17=2.18282" " "#units

After the equations for the lines from A to B and the line from C perpendicular to line AB are obtained, the intersection point of the two equations—the necessary point D—must be solved simultaneously.

Two-point form line from A(1, 3) to B(9, 5):

#(y-y_a)=((y_b-y_a)/(x_b-x_a))(x-x_a)#
#(y-3)=((5-3)/(9-1))(x-1)#
#y-3=1/4(x-1)#
#4y-12=x-1# #x-4y=-11" " "#first equation
To solve for line from C perpendicular to line AB, use slope #=-4# and point C(6, 2)

Applying the point-slope form

#y-y_c=m(x-x_c)#
#y-2=-4(x-6)#
#y-2=-4x+24#
#4x+y=26" " "#second equation

To determine the unknown point D, simultaneously solve the first and second equations.

You should obtain #(x_d, y_d)=(93/17, 70/17)#
length#=sqrt((x_d-x_c)^2+(y_d-y_c)^2)#
length#=sqrt((93/17-6)^2+(70/17-2)^2)#
length#=sqrt((-9/17)^2+(36/17)^2)#
length#=sqrt((9^2/289+(9^2*4^2)/289)#
length#=9*sqrt(17/289)#
length#=9*sqrt(1/17)#
length#=(9sqrt17)/17=2.18282" " "#units

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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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