Question

The value for x for which the distance between the points F(2,-3) and C (x,5) is 10.
i) 8 or -4 ii) 4 or 8 iii) 5 or -10 iv) 5 or 10

Answer 1

☯ Given,

• Points are, F(2, -3) & C(x , 5).
• Distance between them is 10.

☯ To Find,

• The value of x.

☯ Solution,

Using distance formula,

d = √(x2 - x1)² + (y2 - y1)²

.°. FC = √(x2 - x1)² + (y2 - y1)²

⇒ 10 = √(x - 2)² + (5 - (-3)²

⇒ 10 = √(x - 2)² + (5 + 3)²

⇒ 10 = √(x - 2)² + (8)²

⇒ 10 = √(x - 2)² + 64

⇒ 10 = √x² - 4x + 4 + 64

Squaring on both sides, we get;

⇒ 100 = x² - 4x + 68

⇒ 100 - 68 = x² - 4x

⇒ 32 = x² - 4x

⇒ x² - 4x - 32 = 0

Splitting middle term,

⇒ x² + 4x - 8x - 32 = 0

⇒ x(x + 4) - 8(x + 4) = 0

⇒ (x - 8) (x + 4) = 0

⇒ x = 8 & -4

☯ Hence,

The value of x is 8 & -4.

Answer 2

Answer:

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Step-by-step explanation:

the value of 8 is -4