Questions: Find the distance between the given points. Round to the nearest hundredth. (-4,7) and (3,-5) Find the midpoint of the line segment connecting the given points.

Solution Steps

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

To find the midpoint of the line segment connecting two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the midpoint formula: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

To find the distance between the points \((-4, 7)\) and \((3, -5)\), we use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the given points: \[ \text{Distance} = \sqrt{(3 - (-4))^2 + (-5 - 7)^2} = \sqrt{(3 + 4)^2 + (-5 - 7)^2} = \sqrt{7^2 + (-12)^2} = \sqrt{49 + 144} = \sqrt{193} \approx 13.89 \]

To find the midpoint of the line segment connecting the points \((-4, 7)\) and \((3, -5)\), we use the midpoint formula: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting the given points: \[ \text{Midpoint} = \left( \frac{-4 + 3}{2}, \frac{7 - 5}{2} \right) = \left( \frac{-1}{2}, \frac{2}{2} \right) = \left( -0.5, 1.0 \right) \]

Final Answer