Question

14.
7. The straight line joining (1, 2) and (2, -2) is per-
pendicular to the line joining (8, 2) and (4, p). What
will be the value of p?
(a) -1
(b) 1
(C) 3
(d) None of these

Answer 1

Answer:

(b )  1

Step-by-step explanation:

Answer 2

The answer is option (b) 1

Given: The straight line joining (1, 2) and (2, -2) is perpendicular to the line joining (8, 2) and (4, p)

To find: The value of p

Solution:

Note:

• slope of a line joining (x₁, y₁) and (x₂, y₂) is  (y₂ - y₁) / (x₂ - x₁)
• Product of  slopes of two perpendicular line is -1

Using above statements we will find the value of p

Now find slopes of lines

Slope of straight line joining (1, 2) (2, -2) = (-2 - 2) / (2 - 1) = -4/1 = $- 4$

Slope of straight line joining (8, 2) and (4, p) = (p - 2) / (4 - 8) = (p - 2)/-4  

Product of slopes will be -1

⇒ -4 $[ \frac{(p-2)}{-4}]$ = - 1

⇒ p - 2 = - 1

⇒ p = 2 - 1 = 1

Therefore, the value of p = 1

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