Question

The line L is perpendicular to line M. M passes through (-3,7) and (2,-9). L passes through the midpoint of M. Find the area of the triangle made between L, y axis and x axis

Answer 1

Answer:

1.1390625

Step-by-step explanation:

The area will be half the magnitude of the product of the x- and y-intercepts. Those interceps can be found from the equation of the perpendicular bisector of M.

The midpoint of M is ...

... ((-3, 7) + (2, -9))/2 = (-0.5, -1)

From one end of M to the other, the change in x is 2-(-3) = 5. The corresponding change in y is -9-7 = -16. For change values ∆x and ∆y and midpoint (h, k), the perpendicular bisector through (h, k) can be written ...

... ∆x(x -h) +∆y(y -k) = 0

For our numbers, this is

... 5(x +0.5) -16(y +1) = 0

... 5x -16y = 13.5 . . . . . simplified, almost standard form

... 10x -32y = 27 . . . . . in standard form

We can benefit by putting this equation into intercept form. Dividing by 27 does it.

... x/(27/10) -y/(27/32) = 1

The x-intercept is 27/10 = 2.7; the y-intercept is -27/32 = 0.84375. The enclosed area is half the product of the magnitudes of these values:

... Area = (1/2)(27/10)(27/32) = 729/640 = 1.1390625

_____

In the attachment, the area is rounded to 5 decimal places.