Question

i can find the distance between two given points. find the distance between the given points. 9. a(5, - 1) and b(7, 9)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 5,y_1=- 1,x_2 = 7,y_2 = 9$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=7 - 5=2$, $y_2 - y_1=9-( - 1)=9 + 1 = 10$.

Step3: Square the differences

$(x_2 - x_1)^2=2^2 = 4$, $(y_2 - y_1)^2=10^2 = 100$.

Step4: Sum and square - root

Add the squared differences: $(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 100=104$. Then $d=\sqrt{104}=\sqrt{4\times26}=2\sqrt{26}$.

Answer:

$2\sqrt{26}$