Question

match the expressions on the left which represent distance between two points, with their corresponding points on the right. drag & drop the answer

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Analyze \(\sqrt{(-1 + 1)^2+(-7 + 3)^2}\)

For the points \((-1,-3)\) and \((-1,-7)\), \(x_1=-1,y_1 = - 3,x_2=-1,y_2=-7\). Then \(x_2 - x_1=-1+1\), \(y_2 - y_1=-7 + 3\). So it matches \((-1,-3),(-1,-7)\).

Step3: Analyze \(\sqrt{(2 - 5)^2+(0 - 4)^2}\)

For the points \((5,4)\) and \((2,0)\), \(x_1 = 5,y_1=4,x_2=2,y_2 = 0\). Then \(x_2 - x_1=2 - 5\), \(y_2 - y_1=0 - 4\). So it matches \((5,4),(2,0)\).

Step4: Analyze \(\sqrt{(0 - 4)^2+(-8 + 2)^2}\)

For the points \((4,-2)\) and \((0,-8)\), \(x_1 = 4,y_1=-2,x_2=0,y_2=-8\). Then \(x_2 - x_1=0 - 4\), \(y_2 - y_1=-8 + 2\). So it matches \((4,-2),(0,-8)\).

Step5: Analyze \(\sqrt{(5 - 3)^2+(6 - 1)^2}\)

For the points \((3,1)\) and \((5,6)\), \(x_1 = 3,y_1=1,x_2=5,y_2 = 6\). Then \(x_2 - x_1=5 - 3\), \(y_2 - y_1=6 - 1\). So it matches \((3,1),(5,6)\).

Answer:

\(\sqrt{(-1 + 1)^2+(-7 + 3)^2}\) matches \((-1,-3),(-1,-7)\); \(\sqrt{(2 - 5)^2+(0 - 4)^2}\) matches \((5,4),(2,0)\); \(\sqrt{(0 - 4)^2+(-8 + 2)^2}\) matches \((4,-2),(0,-8)\); \(\sqrt{(5 - 3)^2+(6 - 1)^2}\) matches \((3,1),(5,6)\)