Question

If the distance between the point (4,k)
and (1,0) is 5, then what is the
value of k?​

Answer 1

Answer:

k = 4

Step-by-step explanation:

The points are (4,k) and (1,0).

Let x1 = 4, x2 = 1, y1 = k, y2 = 0

The distance between these 2 points is 5.

Distance = √(x2 - x1)² + (y2 - y1)²       # Using the distance formula

5 = √(1 - 4)² + (0 - k)²

5 = √(-3)² + (-k)²

(5)² = 9 + k²

25 - 9 = k²

√16 = k

∴ k = 4.

Answer 2

GIVEN :

• The distance between the point (4,k)
• and (1,0) is 5.

TO FIND :

• Value of k = ?

SOLUTION :

Let the points A(4,k) and B(1,0)

The distance AB is 5 units.

By using the distance formula :

➨ AB = $\sf \sqrt{(4 - 1)^2 + (k - 0)^2}$

➨ 5 = $\sf \sqrt{(3)^2 + (k)^2}$

➨ 5 = $\sf \sqrt{9 + (k)^2}$

➨ 25 = 9 + k²

➨ 25 - 9 = k²

➨ 16 = k²

➨ ±4 = k

Therefore, the value of k is +4 and -4.