Question

how may units away from the point $(4,3)$ is the point $(-3,-5)$ on the coordinate plane? (round to the nearest tenth)
answer = units

Explanation:

Step1: Find the differences in x - coordinates and y - coordinates

Let \((x_1,y_1)=(4,3)\) and \((x_2,y_2)=(-3,-5)\).
The difference in x - coordinates: \(\Delta x=x_2 - x_1=-3 - 4=-7\).
The difference in y - coordinates: \(\Delta y=y_2 - y_1=-5 - 3=-8\).

Step2: Apply the distance formula \(d = \sqrt{(\Delta x)^2+(\Delta y)^2}\)

Substitute \(\Delta x=-7\) and \(\Delta y = - 8\) into the formula \(d=\sqrt{(-7)^2+(-8)^2}\).
First, calculate \((-7)^2 = 49\) and \((-8)^2=64\).
Then \(d=\sqrt{49 + 64}=\sqrt{113}\).

Step3: Calculate the value of \(\sqrt{113}\)

\(\sqrt{113}\approx10.6\) (rounded to the nearest tenth)

Answer:

\(10.6\)