Question

Segment AB has point A located at (8,9). If the distance from A to B is 10 units, which of the following could be used to calculate the coordinates for point B​

Answer 1

Answer:

$10=\sqrt{({x-8)^2+(y-9)^2}$

Step-by-step explanation:

The formula for calculating the distance between two points is expressed as:

$D=\sqrt{({x-x_1)^2+(y-y_1)^2}$

Given the following

D = 10units

A = (x1, y1)

x1 = 8

y1 = 9

Substitute the given values into the formula

$10=\sqrt{({x-8)^2+(y-9)^2}$

This gives the required expression

Answer 2

Correct answer: $10 = \sqrt{(x-8)^{2}+(y-9)^{2}}$

Given two distinct Points on a Plane, we can use the Length Equation of the Line Segment, which is an application of the Pythagorean Theorem., as part of our system of equations intended to determine the Coordinates of point B. This equation is presented below:

$l_{AB} = \sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}$ (1)

Where:

$l_{AB}$ - Length of the line segment, in units.

$(x_{A}, y_{A})$ - Coordinates of point A.

$(x_{B}, y_{B})$ - Coordinates of point B.

If we know that $l_{AB} = 10$, $(x_{A}, y_{A}) = (8,9)$ and $(x_{B}, y_{B}) = (x,y)$, then the length equation of the line segment is:

$10 = \sqrt{(x-8)^{2}+(y-9)^{2}}$

We could use $10 = \sqrt{(x-8)^{2}+(y-9)^{2}}$ as part of a system of equation intended to determine the coordinates of point B.

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