If line joining (1, 2) and (7, 6) is perpendicular to line joinin… - Vidyadip

MCQ

If line joining (1, 2) and (7, 6) is perpendicular to line joining (3, 4) and (11, x):

A
12
B
16
✓
-16
D
-12

✓

Answer

Correct option: C.

-16

-16

Solution:
We know, slope of line joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\frac{(\text{y}_{2}-\text{y}_{1})}{(\text{x}_{2}-\text{x}_{1})}$
Lines are perpendicular means $m_1\times m_2 = -1$
$\Rightarrow\big(\frac{\text{x}-4}{11-3}\big), \big(\frac{6-2}{7-1}\big) = -1$
⇒ (x - 4) (4) = (-1) (8) (6)
⇒ x - 4 = -12
⇒ x = -16.

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