# The coordinates of the vertices of a triangle are (1,-2), (9,-2), and (h,k). If the area of the triangle is 40, what are the possible values for k?

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The coordinates of the triangle are (1,-2), (9,-2), and (h,k). The area of the triangle is 40. The distance between (1, -2) and (9, -2) is 8. The equation of the line between (1, -2) and (9, -2) is y = -2.

The length of the line from (h, k) perpendicular to the line y = -2 is:

`|k + 2|/(sqrt 1) = |k + 2|`

The area of the triangle is `(1/2)*8*|k + 2| = 40`

=> 4*(k + 2) = 40 and 4*(-k - 2) = 40

=> k + 2 = 10 and -k - 2 = 10

=> k = 8 and k = -12

**The value of k = 8 and k = -12.**

Area of triangle =1/2base*height

the distance between the base is 1 and 9 on the x-axis=8cm

the height can be used to determine the value of k by finding the height of the triangle using the Area(40) and the half of the base(4cm)

40= 4*h

h=40/4=10.

Therefore, to find the value of k,

find a positive number on the y axis that when -2 is added to, gives 10

the answer is 12.

Therefore, the value of k=12.

I hope this helps