To find the distance between the points [tex]\( R(-1, 1) \)[/tex] and [tex]\( S(-4, -5) \)[/tex], we can use the distance formula. The distance [tex]\( d \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, the coordinates of [tex]\( R \)[/tex] are [tex]\((-1, 1)\)[/tex] and the coordinates of [tex]\( S \)[/tex] are [tex]\((-4, -5)\)[/tex]. Let's find the differences in the x-coordinates and y-coordinates first:
[tex]\[ \Delta x = x_2 - x_1 = -4 - (-1) = -4 + 1 = -3 \][/tex]
[tex]\[ \Delta y = y_2 - y_1 = -5 - 1 = -5 - 1 = -6 \][/tex]
Now we plug these differences into the distance formula:
[tex]\[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} \][/tex]
[tex]\[ d = \sqrt{(-3)^2 + (-6)^2} \][/tex]
[tex]\[ d = \sqrt{9 + 36} \][/tex]
[tex]\[ d = \sqrt{45} \][/tex]
Using a calculator or simplifying further, we find the square root of 45 as approximately [tex]\( 6.708203932499369 \)[/tex].
To the nearest tenth, this value is rounded to [tex]\( 6.7 \)[/tex].
Thus, the distance between the points [tex]\( R \)[/tex] and [tex]\( S \)[/tex] is [tex]\( 6.7 \)[/tex]. The correct answer is [tex]\( 6.7 \)[/tex].
