Question

what is the distance between the points (3, 4) and (7, 1)? a. 5 b. 6 c. $sqrt{35}$ d. $sqrt{20}$ what is the sum of the squares of the differences in coordinates if the x - difference is 3 and the y - difference is 4? a. 25 b. 20 c. 10 d. 7

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(7,1)$. So $x_2 - x_1=7 - 3 = 4$ and $y_2 - y_1=1 - 4=- 3$. Then $d=\sqrt{4^2+( - 3)^2}=\sqrt{16 + 9}=\sqrt{25}=5$.

Step2: Calculate sum of squares of differences

Given $x -$difference is 3 and $y -$difference is 4. The sum of the squares of the differences is $3^2+4^2=9 + 16=25$.

Answer:

1. A. 5
2. A. 25