How might you prove your observations in Question 2 using algebra and x and y-coordinates? Briefly outline an approach using wha

Question

grandymaker [24]

3 years ago

8

How might you prove your observations in Question 2 using algebra and x and y-coordinates? Briefly outline an approach using wha

t you know about a midpoint and the slope of a line.

Mathematics

2 answers:

tresset_1 [31] · Answer 1 · 2022-10-06T09:46:06+03:00

Answer:

I can use variables to represent the coordinates of the vertices for a general triangle, ∆ABC. Then I can calculate the midpoints of the sides in terms of those variables. Using the point-slope formula for the equation of a straight line, I can build the symbolic equations for the three medians, AE, BF, and CD. I can solve for the point of intersection for two of the medians, AE and BF, for example. Finally, I can prove the lines (i.e., medians) concurrent if the point I found also satisfies the equation of the line for CD.

Harrizon [31] · Answer 2 · 2022-10-06T11:39:02+03:00

Answer:

I can use variables to represent the coordinates of the vertices for a general triangle, ∆ABC. Then I can calculate the midpoints of the sides in terms of those variables. Using the point-slope formula for the equation of a straight line, I can build the symbolic equations for the three medians, AE, BF, and CD. I can solve for the point of intersection for two of the medians, AE and BF, for example. Finally, I can prove the lines (i.e., medians) concurrent if the point I found also satisfies the equation of the line for CD.

Step-by-step explanation:

Here is the answer from Plato! Hope this helps :)