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The line L passes through the points P(1,2) and Q(5,−2).
Find the slope of L.
Determine an equation for L in the form y=mx+c.
Find the midpoint of [PQ].
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The line L1 passes through the points A(1,−2) and B(1,3).
Write down the equation of L1.
A second line, L2, is perpendicular to L1 and passes through C(−4,5).
Find the equation of L2 in the form y=mx+c.
The point P lies on L1, and the point Q lies on L1 and L2.
Given that P is equidistant from A and Q, find the coordinates of P.
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The point U has coordinates (6,−3) and the point V has coordinates (−2,7). The point W has coordinates (1,−1).
Write down the coordinates of X, the midpoint of line segment UV.
Find the gradient of the line WX.
Find the equation of WX. Write your answer in the form
where a,b,d∈Z.
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In this question, distances are measured in meters.
A zip-line crossing a crocodile infested river can be modeled as a straight line between (0,28) and (50,20). The left and right banks of the river lie at (10,0) and (30,0), respectively.
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Calculate the length of the zip-line.
Determine the minimum vertical distance from the zip-line to the river.
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