The following table shows the coordinates of points S, M and T. In each case, state whether M Class 9

The following table shows the coordinates of points S, M and T. In each case, state whether M Class 9

Question 1.

The following table shows the ! coordinates of points S, M and T. In each case, state whether M is the midpoint ; of segment ST. Justify your answer. Class 9

When M is the mid-point of ST, can you ! find any connection between the coordinates of M, S and T?

Solution:

When M is the midpoint of ST, then SM = MT

i. SM = $\sqrt{(-3-0)^2+(0-0)^2}$ = 3 units

MT = $\sqrt{(3-0)^2+(0-0)^2}$ = 3 units

∴ SM = MT

∴ M is the midpoint of ST

ii. SM = $\sqrt{(3-2)^2+(4-3)^2}$ = $\sqrt{2}$ units

MT = $\sqrt{(4-3)^2+(5-4)^2}$ = $\sqrt{2}$ units

∴ SM = MT

∴ M is the midpoint of ST

iii. SM = $=\sqrt{(0-0)^2+(5-0)^2}$ = 5 units

MT = $\sqrt{(0-0)^2+(5+10)^2}$ = 15 units

∴ SM ≠ MT

∴ M is not the midpoint of ST

iv. SM = $\sqrt{(0+8)^2+(-2-7)^2}$ = $\sqrt{145}$ units

MT = $\sqrt{(6-0)^2+(-3+2)^2}$ = $\sqrt{37}$ units

∴ SM ≠ MT

∴ M is not the midpoint of ST

Now, 3 = $3=\frac{4+2}{2}$ and $4=\frac{5+3}{2}$

We observe that coordinates of midpoint are the average of coordinates of the two endpoints.