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Triangular Slope

Age 14 to 16 Short Challenge Level:

Answer: $\frac 43$ and $-\frac34$


Using scale factors
OA
Red triangles are similar so use scale factor $\frac35=0.6$ to find missing lengths
   
Gradient is $\dfrac{4\times0.6}{3\times0.6}=\dfrac43$

AB
Green triangles are similar with scale factor $\frac45=0.8$
   
Gradient is $\dfrac{-3\times0.6}{4\times0.6}=-\dfrac34$



Using similar and congruent triangles
OA
Red triangles are similar so use large red triangle for the correct ratios
   
Gradient is $\dfrac43$     


AB
   
Gradient is $\dfrac{-3}{4}=-\dfrac34$




You can find more short problems, arranged by curriculum topic, in our short problems collection.