Question

the coordinates of point q are (3, 11). the coordinates of point a are (2, 4). determine the length of segment qa. enter the coordinates of the two given points and then calculate the distance between them. coordinates (x1, y1) of point q: (?,?) coordinates (x2, y2) of point a: (?,?) d = \sqrt{(x2 - x1)^2+(y2 - y1)^2} d = \sqrt{( )^2+( )^2} d = the length of segment qa is feet

Explanation:

Step1: Identify point - Q coordinates

Given point Q has coordinates $(x_1,y_1)=(3,11)$.

Step2: Identify point - A coordinates

Given point A has coordinates $(x_2,y_2)=(2,4)$.

Step3: Substitute into distance formula

Substitute $x_1 = 3,y_1 = 11,x_2 = 2,y_2 = 4$ into $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. We get $d=\sqrt{(2 - 3)^2+(4 - 11)^2}=\sqrt{(-1)^2+(-7)^2}$.

Step4: Calculate the squares

$(-1)^2 = 1$ and $(-7)^2=49$, so $d=\sqrt{1 + 49}$.

Step5: Simplify the square - root

$d=\sqrt{50}=5\sqrt{2}\approx7.07$.

Answer:

The length of segment QA is $5\sqrt{2}\approx7.07$