UPSC NDA Math Model Paper 6

Given: The inclination of the line joining the points (x, - 3) and (2, 5) is 135°
Here, we have to find the value of x.
As we know that, the slope of a line is given by tan α and it is denoted by m where α ≠ π/2 and it represents the angle which a given line makes with respect to the X – axis in the positive direction.
⇒ m = tan (135°) = tan (180° - 135°) = - tan 45° = - 1
As we know that, the slope of the line joining the points (x , y ) and (x , y ) is: m=

y2‌−‌y1

x2−x1

Here, x = x, y = - 3, x = 2, y = 5 and m = - 1.
⇒−1=

5‌−‌(−3)

2−x

⇒ - 2 + x = 8
⇒ x = 10
Hence, option C is the correct answer