Let's analyze Riko's method and then find the correct distance using the appropriate formula.
Riko calculated the distance by adding the absolute values of the y-coordinates:
[tex]\[
|-3| + |-5| = 3 + 5 = 8
\][/tex]
Riko's method is incorrect. He mistakenly added the absolute values of the y-coordinates, which does not give the correct distance between two points. Instead, the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in the coordinate plane should be calculated using the distance formula:
[tex]\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Let’s apply the distance formula to the points [tex]\((-2, -3)\)[/tex] and [tex]\((2, -5)\)[/tex]:
1. Calculate the difference in the x-coordinates:
[tex]\[
x_2 - x_1 = 2 - (-2) = 2 + 2 = 4
\][/tex]
2. Calculate the difference in the y-coordinates:
[tex]\[
y_2 - y_1 = -5 - (-3) = -5 + 3 = -2
\][/tex]
3. Square these differences:
[tex]\[
(x_2 - x_1)^2 = 4^2 = 16
\][/tex]
[tex]\[
(y_2 - y_1)^2 = (-2)^2 = 4
\][/tex]
4. Add the squares of the differences:
[tex]\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 16 + 4 = 20
\][/tex]
5. Take the square root of the sum:
[tex]\[
\text{Distance} = \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} \approx 4.472
\][/tex]
Thus, the correct distance between the points (-2, -3) and (2, -5) is approximately [tex]\(4.472\)[/tex] units.
In conclusion, Riko is incorrect because he did not use the distance formula. He added the absolute values of the y-coordinates instead of calculating the actual Euclidean distance. The correct distance is approximately [tex]\(4.472\)[/tex] units.
