Question

a right angle is formed by the x-axis, and the line y = -3x + 6. what is the length of the hypotenuse?

Answer 1

The length of the hypotenuse is
`2√(10)` ≅ 6.325

Explanation:

∵ A right angle is formed by the x-axis, y-axis and the line y = -3x + 6

∴ The line intersected the x-axis at point (x, 0)

→ To find x substitute y in the equation by 0

∵ 0 = -3x + 6

→ Add 3x to both sides

∴ 0 + 3x = -3x + 3x + 6

∴ 3x = 6

→ Divide both sides by 3

∵
`(3x)/(3)=(6)/(3)`

∴ x = 2

∴ The line intersected the x-axis at point (2, 0)

∵ The line intersected the y-axis at point (0, y)

→ Substitute x in the equation by 0 to find y

∴ y = -3(0) + 6

∵ y = 0 + 6

∴ y = 6

∴ The line intersected the xyaxis at point (0, 6)

∵ The endpoints of the hypotenuse are (2, 0) and (0, 6)

→ Use the rule of the distance d =
`\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}` to find it

∵ x1 = 2 and y1 = 0

∵ x2 = 0 and y2 = 6

∴ h =
`\sqrt{(0-2)^(2)+(6-0)^(2)}=√(4+36)=√(40)=2√(10)`

∴ The length of the hypotenuse is
`2√(10)` ≅ 6.325

The attached figure for more understanding