Question

Calculate the distance between the points E=(-2,-5) and M=(0, 3) in the coordinate plane.

a) 5 units
b) 7 units
c) 8 units
d) 10 units

Answer 1

The correct answer should be the distance calculated using the distance formula which gives approximately 8.246 units.

Step-by-step explanation:

The correct answer is option a) 5 units. To calculate the distance between two points in the coordinate plane, use the distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

For points E=(-2,-5) and M=(0, 3), apply the formula:

1. Calculate the difference in x-coordinates: (0 - (-2)) = 2.
2. Calculate the difference in y-coordinates: (3 - (-5)) = 8.
3. Square each difference: \(2^2 = 4\) and \(8^2 = 64\).
4. Add the squares: 4 + 64 = 68.
5. Take the square root: \(\sqrt{68}\) which simplifies to \(\sqrt{64 + 4}\) = \(\sqrt{64} + \sqrt{4}\) = 8 + 2 = 10, but since we only need the principal square root for distance, it is simply \(\sqrt{68}\) which is roughly 8.246 or approximately 8 (not an option).

However, we must recognize an error here and observe that the square root of 68 is not 10, but rather approximately 8.246, which is closer to 8 than to any other options provided.

Therefore, a recalculated assessment, considering the nearest whole number, will indicate that the distance is closer to 8 units, which is not listed as an option. This indicates that there may be a mistake in the options provided.