Question

1. points a, b, c, and d are vertices of a square. point e is inside the square. explain how to tell whether point e is closer to a, b, c, or d.

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let \(A=(x_A,y_A)\), \(B=(x_B,y_B)\), \(C=(x_C,y_C)\), \(D=(x_D,y_D)\) and \(E=(x_E,y_E)\).

Step2: Calculate distances \(EA\), \(EB\), \(EC\) and \(ED\)

• \(EA=\sqrt{(x_E - x_A)^2+(y_E - y_A)^2}\)
• \(EB=\sqrt{(x_E - x_B)^2+(y_E - y_B)^2}\)
• \(EC=\sqrt{(x_E - x_C)^2+(y_E - y_C)^2}\)
• \(ED=\sqrt{(x_E - x_D)^2+(y_E - y_D)^2}\)

Step3: Compare the distances

Compare the values of \(EA\), \(EB\), \(EC\) and \(ED\). The smallest value among them will tell which vertex (\(A\), \(B\), \(C\) or \(D\)) the point \(E\) is closest to.

Answer:

Calculate the distances \(EA\), \(EB\), \(EC\) and \(ED\) using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), then compare these distances. The vertex corresponding to the smallest distance is the one that point \(E\) is closest to.