Question

I need help!! I don’t know which one it is.
Which point is closest to point A?
Point__

Answer 1

Answer: C

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Step-by-step explanation:

Point A is at (-3,3) while point B is at (2,5)

Let's use the distance formula to find the distance between these points.

`A = (x_1,y_1) = (-3,3) \text{ and } B = (x_2, y_2) = (2,5)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-3-2)^2 + (3-5)^2)\\\\d = √((-5)^2 + (-2)^2)\\\\d = √(25 + 4)\\\\d = √(29)\\\\d \approx 5.3852\\\\`

The distance from A to B is approximately 5.3852 units.

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Point C is at (-2,-2)

Let's find the distance from A to C

`A = (x_1,y_1) = (-3,3) \text{ and } C = (x_2, y_2) = (-2,-2)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-3-(-2))^2 + (3-(-2))^2)\\\\d = √((-3+2)^2 + (3+2)^2)\\\\d = √((-1)^2 + (5)^2)\\\\d = √(1 + 25)\\\\d = √(26)\\\\d \approx 5.099\\\\`

The distance from A to C is approximately 5.099 units.

So far, point C is the closest to point A.

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Point D is at (3,3)

We could use the distance formula to find the distance from A to D, but we can simply subtract the x coordinates and make the result positive if needed. This works because points A and D have the same y coordinate.

D - A = 3 - (-3) = 3+3 = 6

The distance from A to D is 6 units.

Or you could count out the horizontal spaces between the points and you should count 6 spaces.

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Summary:

• Distance from A to B = 5.3852 (approximate)
• Distance from A to C = 5.099 (approximate)
• Distance from A to D = 6 (exact)

The smallest distance value is the 5.099, which is from A to C.

Therefore, point C is closest to point A.

Answer 2

Point D

Step-by-step explanation:

The length from Point A to Point D is 6 units, while the length from point A to Point C is 7 units, and the length from Point A to Point B is also 7 units. Because to reach Point C, you have to make one turn, adding one more unit. Same with Point B.