To find the distance between the two points \((3, -5)\) and \((-2, -7)\) on the coordinate plane, we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (3, -5)\) and \((x_2, y_2) = (-2, -7)\).
Let's substitute these values into the formula:
-
Calculate \(x_2 - x_1\): \[ x_2 - x_1 = -2 - 3 = -5 \]
-
Calculate \(y_2 - y_1\): \[ y_2 - y_1 = -7 - (-5) = -7 + 5 = -2 \]
-
Now square these differences: \[ (x_2 - x_1)^2 = (-5)^2 = 25 \] \[ (y_2 - y_1)^2 = (-2)^2 = 4 \]
-
Add these squares: \[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 25 + 4 = 29 \]
-
Now take the square root to find the distance: \[ d = \sqrt{29} \]
We approximate \(\sqrt{29}\). It lies between \(\sqrt{25} = 5\) and \(\sqrt{36} = 6\), and we can find it using a calculator:
\[ \sqrt{29} \approx 5.385 \]
To round this distance to the nearest tenth, we observe the first decimal digit:
\[ 5.385 \approx 5.4 \text{ when rounded to the nearest tenth} \]
Thus, the distance between the points \((3, -5)\) and \((-2, -7)\) rounded up to the nearest tenth of a unit is
\[ \boxed{5.4} \]
1 answer