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6. Use Structure Point B has coordinates (-4,-2). The x coordinate of point A is 5. The distance between point A and point B is 15 units.

a. What are the possible coordinates of
point A?

b. Find the possible coordinates of point A
if point B were moved to (-7, -2).
ei Olog bris 9.3
4mb ST

1 Answer

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a. To find the possible coordinates of point A, we know that the x-coordinate of point A is 5 and the distance between point A and point B is 15 units. Since the x-coordinate of point B is -4, we can calculate the difference between the x-coordinates of point A and point B:

x-coordinate of point A - x-coordinate of point B = 5 - (-4) = 9

So, the possible x-coordinate of point A is 9.

Now, we can use the distance formula to find the possible y-coordinate of point A. The distance between point A (5, y) and point B (-4, -2) is given as 15 units:

√[(x2 - x1)^2 + (y2 - y1)^2] = 15

Plugging in the coordinates of the points:

√[(5 - (-4))^2 + (y - (-2))^2] = 15

Simplifying:

√[9^2 + (y + 2)^2] = 15

Squaring both sides:

81 + (y + 2)^2 = 225

Solving for (y + 2)^2:

(y + 2)^2 = 225 - 81

(y + 2)^2 = 144

Taking the square root:

y + 2 = ±12

Solving for y:

y = -2 ± 12

This gives us two possible y-coordinates:

y = -2 + 12 = 10

y = -2 - 12 = -14

Therefore, the possible coordinates of point A are (9, 10) and (9, -14).

b. If point B were moved to (-7, -2), we follow the same process as above.

The x-coordinate of point A is 5, and the x-coordinate of point B is -7. The difference in x-coordinates is:

x-coordinate of point A - x-coordinate of point B = 5 - (-7) = 12

So, the possible x-coordinate of point A is 12.

Using the distance formula, we have:

√[(12 - (-7))^2 + (y - (-2))^2] = 15

Simplifying:

√[19^2 + (y + 2)^2] = 15

Squaring both sides:

361 + (y + 2)^2 = 225

Solving for (y + 2)^2:

(y + 2)^2 = 225 - 361

(y + 2)^2 = -136

Since the square of a real number cannot be negative, there are no real solutions for (y + 2)^2. Therefore, there are no possible coordinates for point A if point B is moved to (-7, -2).

HOPE THIS HELP :)

User Njeru Cyrus
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