Can anyone please help me with this

[Bettyp615]

the triangle abc which has vertices a(0,0) b (12,0) and c (8,5) will have point d, inside the triangle, that will create the three triangles abc, acd and bcd of equal area. using the area of a triangle, find the coordinates of point D such that the three triangles ACD, ABD and BCD will be of equal area.

 

[tri]

One third of area of ΔABC is the equal area of inner triangles, which can be used to find the altitude of ΔABD, which is the y co-ordinate of point D, and x co-ordinate of point D is the sum of x co-ordinates of points A,B,C divided by 3.


In general,
The centroid of a triangle is:
(x₁+x₂+x₃)/3 , (y₁+y₂+y₃)/3

 

[blamocur]

One third of area of ΔABC is the equal area of inner triangles, which can be used to find the altitude of ΔABD, which is the y co-ordinate of point D, and x co-ordinate of point D is the sum of x co-ordinates of points A,B,C divided by 3.

View attachment 33554
In general,
The centroid of a triangle is:
(x₁+x₂+x₃)/3 , (y₁+y₂+y₃)/3

While correct, it is not obvious to me that the centroid produces equal area triangles.

 

[BigBeachBanana]

While correct, it is not obvious to me that the centroid produces equal area triangles.

See MSE for proof that 3 medians divide a triangle into 6 equal areas.

 

[Dr.Peterson]

the triangle abc which has vertices a(0,0) b (12,0) and c (8,5) will have point d, inside the triangle, that will create the three triangles abc, acd and bcd of equal area. using the area of a triangle, find the coordinates of point D such that the three triangles ACD, ABD and BCD will be of equal area.

You haven't told us what you have learned, which prevents us from helping you effectively. Most likely, you don't know the fact that was assumed in post #2, so that was an inappropriate answer. (We try not to give full answers, which prevent you from making the effort needed in order to learn.)

Can you tell us what facts are available to you?

It is easy to find the y-coordinate of D using only the basic formula for area of a triangle, applied to ABD. For its x-coordinate, you need to think about one of the other areas.

By the way, you should be aware that "a" and "A" are different things in math; the points here are called A, B, and C, so the triangle is ABC, not abc. Sometimes that can be important.

 

[Bettyp615]

Thank you everyone. Sorry I should have said I’m a parent trying to help/ teach my child. But I had no idea if we were on the right track or not.

 

[BigBeachBanana]

Thank you everyone. Sorry I should have said I’m a parent trying to help/ teach my child. But I had no idea if we were on the right track or not.

Can you answer Dr.Peterson's question above? There is more than one way to solve the problem. It's pointless to show you something that you/your child have no understanding of.

It seems that you have tried something already. Please share that. Also, give Dr.Peterson's approach a go. It's probably what s/he expected to do.

 

[blamocur]

See MSE for proof that 3 medians divide a triangle into 6 equal areas.

I've figured out how to prove it, but I did think that it should not be treated as obvious.