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The gradient of a line L through point A(2x,4) and B(-1,x) is 1/ the line perpendicular to L passing through B.

a. True
b. False

User Sili
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1 Answer

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Final answer:

The statement in question is false because the gradient of a line and the gradient of a perpendicular line are negative reciprocals of each other, not reciprocals.

Step-by-step explanation:

The student's question pertains to the relationship between the gradient of a given line L and the gradient of a line perpendicular to it. The question asks for the validation of the statement that the gradient of line L, which passes through points A(2x,4) and B(-1,x), is equal to the reciprocal of the gradient of the line perpendicular to L passing through point B.

To solve this, we first calculate the gradient (slope) of line L.

The slope of line L is given by the formula: slope of L = (y2 - y1)/(x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line. For line L, using points A(2x,4) and B(-1,x), this becomes:

slope of L = (x - 4)/(-1 - 2x)

The slope of a line perpendicular to line L, which we'll call line M, is the negative reciprocal of the slope of line L.

Therefore, if the slope of line L is 'm', the slope of line M will be '-1/m'.

Based on this, the statement in question is false as it incorrectly asserts the slope of line L to be the reciprocal of the slope of line M instead of the negative reciprocal.

User Rafael Steil
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