Question

pythagorean distance
what is the distance c?
points: (4, 5) (-5, -7)
a = δx = 9
b = δy = 12
c = ?
pythagorean formula c² = a² + b²

Explanation:

Step1: Identify the formula

We use the Pythagorean formula \( c^{2}=a^{2}+b^{2} \), where \( a = 9 \) and \( b = 12 \).

Step2: Substitute values

Substitute \( a = 9 \) and \( b = 12 \) into the formula: \( c^{2}=9^{2}+12^{2} \).

Step3: Calculate squares

Calculate \( 9^{2}=81 \) and \( 12^{2}=144 \). Then \( c^{2}=81 + 144=225 \).

Step4: Find c

Take the square root of 225: \( c=\sqrt{225}=15 \). Wait, but let's check again. Wait, \( a = \Delta x=4 - (-5)=9 \), \( b=\Delta y = 5-(-7)=12 \). Then \( c^{2}=9^{2}+12^{2}=81 + 144 = 225 \), so \( c = 15 \). But looking at the options, 15 is present (the 15 in the fifth row, third column). Wait, maybe I made a mistake? Wait no, \( 9^2 + 12^2=81 + 144 = 225 \), square root of 225 is 15. So the correct value of \( c \) is 15.

Answer:

15 (corresponding to the option "15" in the fifth row, third column of the number pad)