Question

If the points (x, y), (2, 3) & (−3, 4) are collinear then (a) x + y = 17 (b) x − y = 17 (c) x − 5y = 17 (d) x + 5y = 17

Answer 1

Answer:

(d)

Step-by-step explanation:

If these points are collinear, their slopes must be equal.

Slope of any two point is given by $(\small{\frac{y_2-y_1}{x_2-x_1})}$

Using this, if both are collinear:

Slope of (x, y) & (2,3)is:$\small{\frac{y-3}{x-2}}$

Slope of (2,3) & (-3,4) = $\small{\frac{4-3}{-3-2}} =\small{\frac{1}{-5}}$

= > (y - 3)/(x - 2) = (-1/5)

= > 5(y - 3)= - (x - 2)

= > 5y - 15 = - x + 2

= > 5y + x = 15 + 2

= > x + 5y = 17