Given points are (h, 3) and (4, 1).
∴ Slope of the line joining (h, 3) & (4, 1)
=

1−3

4−h

=

−2

4−h

... (i)
slope of given line 7x – 9y – 19 = 0 is

7

9

... (ii)
If two lines intersect at right angles, then
(slope of (i)) × (slope of (ii)) = –1
(

−2

4−h

) × (

7

9

) = - 1 ⇒

−14

36−9h

= - 1 ⇒ 14 = 36 - 9h ⇒ 9h = 36 - 14
⇒ 9h = 22 ⇒ h =

22

9