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Question 8 of 10

The distance between the points [tex]\((1,2)\)[/tex] and [tex]\(\left(x_1, y_1\right)\)[/tex] is the square root of [tex]\(\left(x_1-1\right)^2+\left(y_1-2\right)^2\)[/tex].

A. True
B. False

Sagot :

GinnyAnsweridn
To determine whether the statement about the distance between the points [tex]\((1, 2)\)[/tex] and [tex]\((x_1, y_1)\)[/tex] is correct, we need to consider the formula for the Euclidean distance between two points in a 2-dimensional plane.

The formula for the distance [tex]\(d\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Here, the coordinates of the first point are [tex]\((1, 2)\)[/tex], so [tex]\(x_2 = 1\)[/tex] and [tex]\(y_2 = 2\)[/tex]. The coordinates of the second point are [tex]\((x_1, y_1)\)[/tex].

Substituting these points into the distance formula:

[tex]\[ d = \sqrt{(x_1 - 1)^2 + (y_1 - 2)^2} \][/tex]

This matches exactly with the given expression:
[tex]\[ \sqrt{(x_1 - 1)^2 + (y_1 - 2)^2} \][/tex]

Since the given formula correctly represents the Euclidean distance between the two points [tex]\((1, 2)\)[/tex] and [tex]\((x_1, y_1)\)[/tex], the statement is true.

Therefore, the answer is:
A. True
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