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Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 6y = 12 + 2x - 4y$.

User Benawad
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1 Answer

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distance formula = sqrt((x1 - x2)^2 + (y1 - y2)^2)

Answer:

x = 12

y = -6

distance between the x-intercept and the y-intercept is 6√5

Explanation:

To find the x-intercept, we set y = 0 and solve for x:

```

3x - 6(0) = 12 + 2x - 4(0)

3x = 12 + 2x

x = 12

```

Therefore, the x-intercept is (12, 0).

To find the y-intercept, we set x = 0 and solve for y:

```

3(0) - 6y = 12 + 2(0) - 4y

-6y = 12 - 4y

-2y = 12

y = -6

```

Therefore, the y-intercept is (0, -6).

To find the distance between the two intercepts, we can use the distance formula:

```

distance = sqrt((x1 - x2)^2 + (y1 - y2)^2)

```

In this case, (x1, y1) = (12, 0) and (x2, y2) = (0, -6), so the distance is:

```

distance = sqrt((12 - 0)^2 + (0 - (-6))^2)

distance = sqrt(144 + 36)

distance = sqrt(180)

distance = 6 * sqrt(5)

```

Therefore, the distance between the x-intercept and the y-intercept is **6√5**.

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User CodingFrog
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