Answer:
(-5, 11.63) and (-5, -7.63)
Explanation:
To find the coordinates of point A, we need to use the distance formula to find the distance between points A and B, and then use that distance to determine the possible y-coordinates of point A.
The distance between points A and B is given by:
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) are the coordinates of point A and (x₂, y₂) are the coordinates of point B. We know that the x-coordinate of point A is -5, and the coordinates of point B are (3, 2). So we can plug these values into the distance formula:
distance = √[(3 - (-5))² + (2 - y)²]
Simplifying the expression inside the square root:
distance = √[64 + (2 - y)²]
Now we need to find the possible values of y that make the distance equal to 13. We can set up an equation:
√[64 + (2 - y)²] = 13
Squaring both sides:
64 + (2 - y)² = 169
Expanding the square:
64 + 4 - 4y + y² = 169
Rearranging the terms:
y² - 4y - 101 = 0
Using the quadratic formula:
y = (4 ± √(4² - 4(1)(-101))) / (2(1))
Simplifying:
y = (4 ± √409) / 2
So the possible y-coordinates of point A are:
y = (4 + √409) / 2 ≈ 11.63
y = (4 - √409) / 2 ≈ -7.63
Therefore, the possible coordinates of point A are (-5, 11.63) and (-5, -7.63).