Question

find the distance between the points (4, -3) and (4, 7). distance:

Explanation:

Step1: Identify the coordinates

The two points are \((4, -3)\) and \((4, 7)\). So, \(x_1 = 4\), \(y_1=-3\), \(x_2 = 4\), \(y_2 = 7\).

Step2: Use the distance formula (or notice vertical line)

Since the \(x\)-coordinates are the same (\(x_1=x_2 = 4\)), the distance is the absolute difference of the \(y\)-coordinates. The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Substituting the values: \(d=\sqrt{(4 - 4)^2+(7-(-3))^2}=\sqrt{0 + 10^2}=\sqrt{100}=10\). Or, since it's a vertical line, distance \(=|y_2 - y_1|=|7-(-3)| = 10\).

Answer:

10