Question

Find all possible values of a for which for distance between the points A(a, -1) and B(5, 3) is 5 units.

Answer 1

Answer:

a = 8 or a = 2

Step-by-step explanation:

Distance formula = √{(x2 - x1)² + (y2 - y1)²}

where,

first point (x1, y1) & second point (x2, y2)

Using the same formula,

Distance between AB = √{(x2 - x1)² + (y2 - y1)²}

5 = √{(5 - a)² + (3 - [-1])²}

25 = (5 - a)² + (3+1)²    .......Taking square roots on both the sides

25 = 25 - 10a + a² + 4²

25-25 =  a² - 10a + 16

a² - 10a + 16 = 0

a² - 8a -2a + 16 = 0

a (a-8) -2 (a-8) = 0

(a-8) = 0 or (a-2) = 0

a = 8 or a = 2