If points (1, 2) (– 5, 6) and (a, – 2) are collinear, then a =

To determine the value of "a" if the points (1, 2), (-5, 6), and (a, -2) are collinear, we can use the concept of slope.

Step 1: Find the slope between the first two points. The slope between two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1)

Using the points (1, 2) and (-5, 6), we have: slope = (6 - 2) / (-5 - 1) slope = 4 / -6 slope = -2/3

Step 2: Check if the third point lies on the same line. To check if the third point (a, -2) lies on the same line, we need to calculate the slope between the first point (1, 2) and the third point (a, -2). This slope should be equal to the slope calculated in step 1.

Using the points (1, 2) and (a, -2), we have: slope = (-2 - 2) / (a - 1) slope = -4 / (a - 1)

Step 3: Equate the slopes and solve for "a". Since the points are collinear, the slopes between any two points on the line should be equal. Therefore, we can equate the slopes calculated in step 1 and step 2:

-2/3 = -4 / (a - 1)

To solve for "a", we can cross-multiply and simplify the equation:

-2(a - 1) = -12 -2a + 2 = -12 -2a = -14 a = 7

Therefore, if the points (1, 2), (-5, 6), and (a, -2) are collinear, then a = 7.