An equilateral triangle ABC has its centroid at the the origin and the base BC lies along #x+y+1=0#. Gradient of the other two lines are?
For your Info
Ans #2+sqrt3, 2sqrt3#
For your Info
Ans
By signing up, you agree to our Terms of Service and Privacy Policy
Since the centroid of an equilateral triangle divides each median into segments with a ratio of 2:1, the midpoint of the base BC is also the centroid of the triangle.
Given that the base BC lies along the line (x + y + 1 = 0), its midpoint is the centroid, which is at the origin (0,0).
So, the coordinates of point B and C are (B(2, 2)) and (C(2, 2)).
Now, we can find the gradients of the lines AB and AC:

Gradient of AB: [ m_{AB} = \frac{{y_B  y_A}}{{x_B  x_A}} = \frac{{2  0}}{{2  2}} = \frac{1}{2} ]

Gradient of AC: [ m_{AC} = \frac{{y_C  y_A}}{{x_C  x_A}} = \frac{{2  0}}{{2  2}} = \frac{1}{2} ]
So, the gradients of the lines AB and AC are both ( \frac{1}{2} ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 A line passes through #(9 ,3 )# and #( 4, 5 )#. A second line passes through #( 7, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
 A line passes through #(2 ,8 )# and #(4 ,5 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?
 Circle A has a center at #(9 ,4 )# and a radius of #3 #. Circle B has a center at #(1 ,6 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?
 What is the midpoint of the segment whose endpoints are (1, 4) and (3, 6)?
 A line passes through #(3 ,2 )# and #(7 ,3 )#. A second line passes through #(1 , 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7