Are the points M (-3, -4), A (0, 0) and G (6, 8) on the same straight line? Suggest a method Class 9

Are the points M (-3, -4), A (0, 0) and G (6, 8) on the same straight line? Suggest a method Class 9

Question 1.

Are the points M (-3, -4), A (0, 0) and G (6,8) on the same straight line? Suggest a method to check this without plotting and joining the points. Class 9

Solution:

We know that distance between two points

$\begin{aligned} &=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} \\ & \begin{aligned} \mathrm{AM} & =\sqrt{(-3-0)^2+(-4-0)^2} \\ & =\sqrt{9+16} \\ & =\sqrt{25} \\ & =5 \text { units } \\ \mathrm{AG} & =\sqrt{(6-0)^2+(8-0)^2} \\ & =\sqrt{36+64} \\ & =\sqrt{100}=10 \text { units } \\ \mathrm{GM} & =\sqrt{(-3-6)^2+(-4-8)^2} \\ & =\sqrt{81+144} \\ & =\sqrt{225}\end{aligned}\end{aligned}$

= 15 units

∴ GM = AM + AG

∴ Point A is between points M and G.

∴ Points M, A and G are on the same straight line.