Answer:
The length of the hypotenuse is
≅ 6.325
Step-by-step 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
∵ ![\frac{3x}{3}=\frac{6}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B6%7D%7B3%7D)
∴ 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 =
to find it
∵ x1 = 2 and y1 = 0
∵ x2 = 0 and y2 = 6
∴ h = ![\sqrt{(0-2)^{2}+(6-0)^{2}}=\sqrt{4+36}=\sqrt{40}=2\sqrt{10}](https://tex.z-dn.net/?f=%5Csqrt%7B%280-2%29%5E%7B2%7D%2B%286-0%29%5E%7B2%7D%7D%3D%5Csqrt%7B4%2B36%7D%3D%5Csqrt%7B40%7D%3D2%5Csqrt%7B10%7D)
∴ The length of the hypotenuse is
≅ 6.325
<em>The attached figure for more understanding</em>