Emmatex Consult
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16, Adeolu Street Papa-Ajao Mushin, Ipokia
234
ZH1313
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❣️PURE MATHEMATICS❣️
Let's prove that when two straight lines meet, then they are perpendicular to each other and if the gradient of one is m then the other is -1/m. So, their product is -1.
From the diagram,
/AB/ and /CD/ meets at E
Also, F meets E from the x - axis
Clearly, a + b = 90° then a + @ = 90
So, b=@ ........ *
Now, the gradient of AB= FE/GF = tan@ (say m)
Again, gradient of CD = - FE/FH = -1/tanb
recall from * that b = @
So, tanb = tan@ = m
Then the gradient of CD = -1/m
The product of the gradients are m • (-1/m) = -1.
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