The line through (h, 3) and (4, 1) intersects the line 7x – 9y – 1

1.	The line through (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0 at right angle. Find the value of h.
Answer» Given: A (h,3) and B (4,1) be the points intersect At right angle at the line 7x – 9y – 19 = 0 To find: The value of h. Explanation: The line 7x − 9y − 19 = 0 can be written as \(y = \frac{7}{9}x-\frac{19}{9}\) So, the slope of this line is \(\frac{7}{9}\) It is given that the line joining the points A (h,3) and B (4,1) is perpendicular to the line 7x − 9y − 19 = 0. \(\frac{7}{9}\times \frac{1-3}{4-h} = -1\) ⇒ 9h – 36 = -14 ⇒ 9h = 22 ⇒ h = \(\frac{22}{9}\) Hence, the value of h is \(\frac{22}{9}\)

The line through (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0 at right angle. Find the value of h.

Answer»

Given: A (h,3) and B (4,1) be the points intersect At right angle at the line 7x – 9y – 19 = 0

To find:

The value of h.

Explanation:

The line 7x − 9y − 19 = 0 can be written as

\(y = \frac{7}{9}x-\frac{19}{9}\)

So, the slope of this line is \(\frac{7}{9}\)

It is given that the line joining the points A (h,3) and B (4,1) is perpendicular to the line 7x − 9y − 19 = 0.

\(\frac{7}{9}\times \frac{1-3}{4-h} = -1\)

⇒ 9h – 36 = -14

⇒ 9h = 22

⇒ h = \(\frac{22}{9}\)

Hence, the value of h is \(\frac{22}{9}\)