Answer:
The total length (in units) of the biking trail is 17 units.
Step-by-step explanation:
o find distance between points A(x¹, y¹) and B(x², y²), we use formula:
[tex]d = \sqrt{(x^{2}-x^{1})^{2}+(y^{2}-y^{1})^{2}}[/tex]
The trail starts at P(−2, 2) and goes to Q(5, 2).
So, the distance PQ will be calculated as:
[tex]PQ = \sqrt{(5^{}-(-2)^{})^{2}+(2^{}-2^{})^{2}[/tex]
[tex]PQ = \sqrt{(49^{}+0)[/tex]
PQ = 7 units
Then the trail goes from Q(5, 2) to R(5, −5).
So, the distance QR will be calculated as:
[tex]QR = \sqrt{(x^{2}-x^{1})^{2}+(y^{2}-y^{1})^{2}}[/tex]
[tex]QR = \sqrt{(5^{}-5^{})^{2}+(-5^{}-2^{})^{2}[/tex]
QR = 7 units
And then from R(5, −5) to S(8, −5).
[tex]RS = \sqrt{(8^{}-5^{})^{2}+(-5^{}-(-5)^{})^{2}}[/tex]
QR = 3 units
Hence, the total length of the biking trail is:
PQ + QR + QR = 7 + 7 + 3 = 17 units
Keywords: distance formula, length
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