Question

i(4,7) u(-6,5) d = \sqrt{( - 4)^2+(6)^2} d = h(0,1) a(6,-3) 14.42

Explanation:

Step1: Recall distance formula

The distance $d$ 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: Identify the points

Let's assume we are finding the distance between two points, say $I(4,7)$ and $H(0,1)$. Here $x_1 = 0,y_1 = 1,x_2=4,y_2 = 7$. Then $x_2 - x_1=4 - 0=4$ and $y_2 - y_1=7 - 1 = 6$. But the formula in the picture has a wrong - sign in the first part. If we correct it for the points $I(4,7)$ and $H(0,1)$, the distance formula gives $d=\sqrt{(4 - 0)^2+(7 - 1)^2}=\sqrt{4^2+6^2}=\sqrt{16 + 36}=\sqrt{52}\approx7.21$.

Step3: Calculate the value

$d=\sqrt{(- 4)^2+6^2}=\sqrt{16 + 36}=\sqrt{52}\approx7.21$

Answer:

$\sqrt{52}\approx7.21$