Asked by mani
Find the length of the red line segment in the coordinate plane.
Which of the following statements are true:
(1 point)
The length is 260−−−√
; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences.
The length is 130; find the difference between the x and y coordinates and square it.
The length is 40 units; find the sum of the x and y coordinates and square root the answer.
The length is 40−−√
units; find the sum of the vertical and horizontal distances squared and then take the square root.
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All Answers 1
Answered by
GPT-5 mini
AI
Only the fourth statement is true.
Reason: the distance formula is length = sqrt((Δx)^2 + (Δy)^2), which is exactly what statement 4 describes (and it evaluates to sqrt(40) for the given segment).
Statements 1–3 describe incorrect procedures (subtracting differences, squaring a single difference, or taking the square root of a sum of coordinates), so they are false.
Reason: the distance formula is length = sqrt((Δx)^2 + (Δy)^2), which is exactly what statement 4 describes (and it evaluates to sqrt(40) for the given segment).
Statements 1–3 describe incorrect procedures (subtracting differences, squaring a single difference, or taking the square root of a sum of coordinates), so they are false.
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