Find the perpendicular distance from a
point (1, 1) to thr line 3x+4y+8=0
Answers
Answer:
Agriculture is one of the major sectors of the Indian economy. It is present in the country for thousands of years. Over the years it has developed and the use of new technologies and equipment replaced almost all the traditional methods of farming. Besides, in India, there are still some small farmers that use the old traditional methods of agriculture because they lack the resources to use modern methods. Furthermore, this is the only sector that contributed to the growth of not only itself but also of the other sector of the country.
Answer:
The line perpendicular to 3x - 4y + 8 = 0 which also passes through the point (1,0) is 4x + 3y - (4*1 + 3*0) = 0 which is 4x + 3y - 4 = 0.
The intersection of the lines 3x - 4y + 8 = 0 and 4x + 3y - 4 = 0 is ((-4×4-(-8)×3)/(3×3-(-4)×4), (-8×4-3×4)/(3×3-(-4)×4)) which is (-8/25, 44/25) which is the nearest point on the line 3x - 4y + 8 = 0 to the point (1,0).
The distance from (1,0) to (-8/25, 44/25) is √((1 - (-8/25))² + (0 - 44/25)²) which is √((33/25)² + (-44/25)²) which is √((1089 + 1936)/625) which is 11/5.
The perpendicular distance from the line 3x - 4y + 8 = 0 to the point (1,0) is 11/5.
OR
The line parallel 3x - 4y + 8 = 0 which also passes through the point (1,0) is 3x - 4y - (3*1 - 4*0) = 0 which is 3x - 4y - 3 = 0, and the distance between the parallel lines is |8 - -3|/√(3²+(-4)²) which is 11/5.