Straight LineHardBloom L3
Question
A piece of cheese is located at $(12,10)$ in a coordinate plane. A mouse is at $(4, - 2)$ and is running up the line $y = - 5x + 18$. At the point ( $a,b$ ), the mouse starts getting farther from the cheese rather than closer to it. The value of $(a + b)$ is:
Options
A.6
B.10
C.18
D.14
Solution
Sol. [Key Concept: The mouse is closest to the cheese at the foot of the perpendicular from the cheese to its path.]
( $a,b$ ) is the foot of ⟂ ar of ( 12,10 ) on the line $y + 5x = 18$
$$\Rightarrow \ \frac{a - 12}{5} = \frac{b - 10}{1} = - \left( \frac{10 + 5(12) - 18}{26} \right) \Rightarrow \ (a,b) = (2,8)$$
Create a free account to view solution
View Solution FreeMore Straight Line Questions
Consider the family of lines x(a + b) + y = 1, where a, b and c are the roots of the equation x3 - 3x2 + x + λ = 0 ...The square of the distance of the point $P(5,6,7)$ from the line $\frac{x - 2}{2} = \frac{y - 5}{3} = \frac{z - 2}{4}$ i...Area of the parallelogram formed by the lines y = mx, y = mx +1, y = nx and y = nx +1 equals...In an isosceles right angled triangle, a straight line drawn from the mid-point of one of equal sides to the opposite an...A straight line cuts the x-axis at point A(1, 0) and y-axis at point B, such that ∠OAB = α(α > ), C is t...