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(04.03 MC) Point A is located at (0, 4), and point C is located at (−3, 5). Find the x value for the point B that is located one fourth the distance from point A to point C.

User Zollnerd
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1 Answer

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First, we need to find the distance between points A and C. We can use the distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

In this case, the x₁ and y₁ coordinates correspond to point A (0, 4) and the x₂ and y₂ coordinates correspond to point C (-3, 5). Plugging in these values, we get:

d = √[(-3 - 0)² + (5 - 4)²]
= √[9 + 1]
= √10

Now, we want to find point B, which is located one fourth of the distance from point A to point C. To do this, we can find the x-coordinate of B by taking one fourth of the distance between the x-coordinates of A and C.

The x-coordinate of A is 0 and the x-coordinate of C is -3. Subtracting these values and multiplying by one fourth, we get:

xB = (0 - (-3)) * 1/4
= 3 * 1/4
= 3/4

So, the x-coordinate for point B is 3/4.
User Shikhanshu
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