Question

Given the distance between (x,1) and (-2,5) is 2 root 7, find the the value of x. Leave your answer in simplified exact form

Answer 1

Answer:

Step-by-step explanation:

Distance = the square root of (x2-x1)2 + (y2-y1)2Added:Distance Formula: Given the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:square root of x2-x1 squared +y2-y1 squared

Answer 2

The value of x is (√12) - 2, when the distance between (x,1) and (-2,5) is 2√7 units.

What is the length of any line on the graph?

The distance or length of any line on the graph,

$d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

where,

d = distance/length of the line between point 1 and 2,

(x₁ , y₁) = coordinate of point 1,

(x₂ , y₂) = coordinate of point 2,

Given that the distance between (x,1) and (-2,5) is 2√7 units. Therefore we can write,

$d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

$2\sqrt7= \sqrt{(x + 2)^2 + (1-5)^2}$

Squaring both the sides of the equation,

$(2\sqrt7)^2= (\sqrt{(x + 2)^2 + (1-5)^2})^2$

4 × 7= (x + 2)² + (-4)²

28 = (x+2)² + 16

28 - 16 = (x+2)²

12 = (x+2)²

x+2 = √12

x = (√12) - 2

Hence, the value of x is (√12) - 2.

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