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The area of the triangle formed by the line \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1 with the coordinate axes isA. abB. 2abC. \(\frac{1}{2}\)abD. \(\frac{1}{4}\)ab |
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Answer» Given: \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1 The given linear equation is in the slope intercept form. Intercept means the distance at which the given equation cuts or meets the coordinate axis. In this problem a & b are the intercepts on the x and y axis respectively. The triangle formed by a straight line with the coordinate axis is a right angled triangle where the angle subtended at origin is 90°. So the length of the x intercepts becomes the perpendicular and y intercept becomes the base of the triangle. We know, Area Of a triangle = \(\frac{1}{2}\) x (perpendicular length) x (base length) So, Area of the triangle becomes \(\frac{1}{2}\)ab The Area of the triangle is \(\frac{1}{2}\)ab |
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