Question

(-4,5) and (5,-7) click twice to draw a line. click a segment to erase it. answer attempt 1 out of 2 leg 1: 12 leg 2: 9 hypotenuse:

Explanation:

Step1: Identify the distance formula for right - angled triangle

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - angled triangle and \(c\) is the hypotenuse. Here \(a = 12\) and \(b=9\).

Step2: Substitute values into the formula

Substitute \(a = 12\) and \(b = 9\) into \(a^{2}+b^{2}=c^{2}\), we get \(12^{2}+9^{2}=c^{2}\). Calculate \(12^{2}=144\) and \(9^{2}=81\). Then \(144 + 81=c^{2}\), so \(c^{2}=225\).

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (as it represents the length of a side), \(c=\sqrt{225}=15\).

Answer:

15