The distance is dilated by a factor of 3, the length of the image of segment CD will be 4(3) which is 12 units
Given the coordinate of the segment CD with endpoints at C(0, 3) and D(0, 7) is expressed as:
If the distance is dilated by a factor of 3, the length of the image of segment CD will be 4(3) which is 12 units
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(3) Differentiating both sides of
with respect to <em>x</em> gives
Solve for d<em>y</em>/d<em>x</em> :
Then the slope of the tangent line to the curve at (1, 9) is
The equation of the tangent line would then be
<em>y</em> - 9 = -2/3 (<em>x</em> - 1) ==> <em>y</em> = -2/3 <em>x</em> + 29/3
(4) The slope of the tangent line to
at a point <em>(x, y)</em> on the curve is
When <em>x</em> = -1, we have a slope of 2/3, so
-(2<em>a</em> + 1)/(-1 - 2)² = 2/3
Solve for <em>a</em> :
-(2<em>a</em> + 1)/9 = 2/3
2<em>a</em> + 1 = -18/3 = -6
2<em>a</em> = -7
<em>a</em> = -7/2
