Question

What are the coordinates of a point in Quadrant III which is 8 units away from point P? Given that point P is 4 units above and 3 units to the left of the origin.

a) (-5, -4)
b) (-3, -2)
c) (-7, -7)
d) (-1, -1)

Answer 1

None of the options provided are correct for a point 8 units away from point P in Quadrant III, as both a) and c) do not satisfy the distance formula when calculated from point P's coordinates (-3, 4).

Step-by-step explanation:

The coordinates of a point in Quadrant III which is 8 units away from point P, where point P is 4 units above and 3 units to the left of the origin, can be determined using the properties of the coordinate plane and the Pythagorean theorem. Since point P is in Quadrant II at coordinates (-3, 4), moving 8 units away into Quadrant III involves traveling in negative x and y directions. Therefore, the coordinates will have both negative x and y values, which exclude options b) and d). Options a) and c) are left, and by using the distance formula √((x_2 - x_1)^2 + (y_2 - y_1)^2) = 8, where (x_1, y_1) represent the coordinates of point P and (x_2, y_2) are the desired coordinates, we find that both options do not satisfy the equation. Thus, none of the options provided are correct for a point 8 units away from point P in Quadrant III.