The point a(-8, 6) is translated using t: (x, y) → (x + 5. y - 4). what is the distance from a to a'?

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The point a(-8, 6) is translated using t: (x, y) → (x + 5. y - 4). what is the distance from a to a'?

Step-by-step explanation:

For this problem, we can simply plug in the coordinate point into the given formula.

(-8, 6) = (-8 + 5, 6 - 4)

(-8, 6) = (-3, 2)

So, A' is at point (-3, 2)

Now, we have to find the distance from A to A'. We can use the distance formula.

[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

[tex]d=\sqrt{(-3-(-8))^2+(2-6)^2}[/tex]

[tex]d=\sqrt{(5)^2+(-4)^2}[/tex]

[tex]d=\sqrt{25+16}[/tex]

[tex]d=\sqrt{41}[/tex]

So, the distance between A and A' is about 6.4 units.

Sqrt(41) is the answer

Translated means the points are moving across the plane without rotating or changing shape. In this case, the x-coordinate would be moving up 5 (x + 5) and the y-coordinate would be moving to the left 4 (y - 4).

A is (-8, 6). A' is the result of the translation from this point. The results of the solution above in A is the point (-3, 2) = A'.

Now you must find the distance between these two coordinates. To find the distance you must use the distance formula: √(x2 - x1)^2 + (y2 - y1)^2. Since you now have two points, A and A', plug these into the distance formula.

√(-3 - (-8))^2 + (2 - 6)^2

√5^2 + (-4)^2

√25 + 16

√41

The distance from A to A' is √41.