Question

Determine whether the given coordinates are the vertices of a triangle. Explain.

L(–24, –19), M(–22 ,20), N(–5, –7)


A:
yes:
LM + MN > LN,
LM + LN > MN,
LN + MN > LM
B:
no:
LM + MN = LN
C:
no:
LM + MN < LN
D:
yes:
LM + MN < LN,
LM + LN < MN,
LN + MN < LM

Answer 1

Answer:
yes
LM + MN > LN,
LM + LN > MN,
LN + MN > LM

Explanation:
In any triangle, the sum of any two sides MUST BE GREATER than the third side.
Therefore, to decide whether the given coordinates can form a triangle or not, we will simply get the length of each side and then check the above condition.

The length can be calculated using the distance formula attached in the image.

LM = $\sqrt{(-24--22)^2+(20--19)^2}$ = 39.05 units
MN = $\sqrt{(-5--22)^2+(-7-20)^2}$ = 31.906 units
NL = $\sqrt{(-5--24)^2+(-7--19)^2}$ = 22.4722 units

Now, let's check:
LM + MN = 39.05 + 31.906 = 70.956 units > NL
MN + NL = 31.906 + 22.4722 = 54.3782 > LM
LM + NL = 39.05 + 22.4722 = 61.5222 > MN

Therefore,, the given coordinates can form a triangle

Hope this helps :)