SOLUTION: how do i do the following problem?
Points D(2,4), E(3,2)and F(4,5) are the midpoints od the sides AC, AB, and BC, respectively, in triangle ABC. Find the coordinates of the vet
Algebra.Com
Question 397985: how do i do the following problem?
Points D(2,4), E(3,2)and F(4,5) are the midpoints od the sides AC, AB, and BC, respectively, in triangle ABC. Find the coordinates of the veticies of the triangle using systems of equations.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Use the fact that a line through two of the midpoints of the sides of a triangle is parallel to the third side of the triangle.
Hence the line containing the segment DE is parallel to the line containing the segment BC. Use the slope formula to calculate the slope of the line containing the segment DE:
Use the fact that the slopes of parallel lines are equal, i.e., 
, the fact that the line containing the segment BC contains the point F, and the point-slope form of an equation of a line to write an equation of the line containing the segment BC:
)
Then put it in Standard Form:
In a similar fashion, determine the slope of the line containing the segment FE so that you can write the equation of the line containing the segment AC, namely:
Now solve the system:
which is perforce a consistent/independent system. The single ordered pair element of the solution set will be the coordinates of the point of intersection of the lines containing segments BC and AC, namely the vertex C of the triangle.
Similarly, determine the standard form equation of the line containing segment AB. That equation plus each of the others already developed will form two additional consistent and independent systems the solution sets of which are the coordinates of points A and B.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
Given Triangle ABC with A(2, 1), B(4, 9) and C(16,1).
a. Find the midpoints of AB, BC,... (answered by mananth)
In triangle ABC,D and E are points on the sides AB and AC respectively such that DE... (answered by MathLover1)
If D , E and F are the midpoints of sides AB , BC , and CA respectively of an isosceles... (answered by ccs2011)
Given: In ∆ABC, X and Y are the midpoints of AB and BC respectively.
Complete the... (answered by Solver92311)
Question : D and E are respectively the points on the sides AB and AC of
a triangle ABC (answered by MathTherapy)
For Each proof Identify the hypothesis, argument, and conclusion.
Given: AB = BC
Prove: (answered by solver91311)
D and E ARE POINTS ON THE SIDES AB AND AC RESPECTIVELY OF TRIANGLE ABC SUCH THAT DE IS... (answered by mananth,KMST)
Given:AB=BC
Prove AC=2BC
1. AB=BC (Given)
2. AB+BC=AC (Segment Addition Postulate)
3. (answered by MathLover1)
If D , E and F are the midpoints of sides AB , BC , and CA respectively of an equilateral (answered by richard1234)
