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.

Given, points $M(-3, -4)$, $A(0, 0)$ and $G(6, 8)$.
To check collinearity, we use the distance formula and verify:

$$MA + AG = MG$$

By distance formula, we have

$$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

$$MA = \sqrt{[0 - (-3)]^2 + [0 - (-4)]^2}$$

$$= \sqrt{(3^2 + 4^2)} = \sqrt{9 + 16}$$

$$= \sqrt{25} = 5$$

$$AG = \sqrt{(6 - 0)^2 + (8 - 0)^2}$$

$$= \sqrt{36 + 64} = \sqrt{100} = 10$$

$$MG = \sqrt{[6 - (-3)]^2 + [8 - (-4)]^2}$$

$$= \sqrt{9^2 + 12^2} = \sqrt{81 + 144}$$

$$= \sqrt{225} = 15$$

$$\text{Now, } MA + AG = 5 + 10 = 15 = MG$$

Hence, the given three points are collinear.

## Concept Applied

Three points are collinear when the sum of the two shorter distances between them is exactly equal to the longest distance.