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1) Find the slope, x-intercept and y-intercept of line 4x - 6y - 24 = 0. {answer should come }

2) Reduce the equation 3x - 2y + 6 = 0 to the double-intercept form and find the x-intercept and y-intercept. {answer should come }

3) Th centroid of a triangle is (1,4) and co-ordinates of two of its vertices are (4,-3) and (-9,7). Find the area of the triangle. (answer should come 183/2)

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4x - 6 y - 24 =0 divide by the constant term and write it so that RHS has value 1. x / 6 - y / 4 = 1 x intercept is 6 and y intercept is 4.

write y term on LHS and x term and constant on the RHS. 6 y = 4 x - 24 => y = 2/3 x - 4 slope is 2/3... OR, slope = - (coeff of x ) / (coeff of y) ========================== 3 x - 2y + 6 = 0 => y / 3 - x / 2 = 1 => x intercept = - 2 and y intercept = 3 =================== x coordinate of centroid = 1 = average of x - coordinates of three vertices y coordinate of centroid = 4 = average of y - coordinates of three vertices

Let the coordinates of the third vertex C be = (x3,y3) 1 = (4-9+x3) / 3 => x = 8 4 = (-3+7+y3) / 3 => y = 0

use the formula for the area of triangle in terms of coordinates of the vertices.

OR, by finding the lengths of sides as, AC² = (8-4)² + (0+3)² = 5² BC² = (8+9)²+(0+7)² = 338 = 13² * 2 AB² = (9+4)²+(7+3)² = 269 s = semi perimeter = (5 + 13√2 + √269) / 2 the area of the triangle could be found using the formula √[ s(s-a)(s-b)(s-c) ]