Question

distance between the points (-4,5)and(12,p)is 10 units. find the value of p​

Answer 1

Answer:

p = 1 or -11

Step-by-step explanation:

Question :-

• Find the value of p for which the distance between the points A(4, -5) and B(12, p) is 10 units.

Solution :-

AB = 10 units

AB² = 100 units

Distance formula :

• $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here :

• $x_1 = 4$

• $x_2 = 12$

• $y_1 = -5$

• $y_2 = p$

Substituting :

• $\sqrt{(12-4)^2+(p-[-5])^2} = 100$

• $\sqrt{(8^2) + (p + 5)^2} = 100$

• $(p + 5)^2 = \sqrt{100-64}$

• $(p + 5)^2 = \sqrt{36}$

• $p + 5 = \±6$

∴ $p = 1\;or\;p = -11$