Question

the line joining A(a,3) to B(2,3) is perpendicular to the line joining C(10,1) to B. Find the value of a

Answer 1

The value of a in the given coordinates is 2.25.

Length of the lines joining the points

Apply Pythagoras theorem to determine the length of the lines.

|AC|² = |AB|²  + |BC|²

(1 - 3)² + (10 - a)² = (3 - 3)² + (2 - a)² + (1 - 3)² + (10 - 2)²

4 + 100 - 20a + a² = 4 - 4a + a² + 4 + 64

104 - 20a + a² = 68 - 4a + a²

104 - 20a  = 68 - 4a

104 - 68 = 20a - 4a

36 = 16a

a = 36/16

a = 2.25

Thus, the value of a in the given coordinates is 2.25.

Learn more about length of lines here: brainly.com/question/1597347

#SPJ1