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

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

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

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

m a t h w a y. c o m

step-by-step explanation: