Question

para que valor de m os pontos(2,1),(m,-2) e(4,-1) sao colineares?​

Answer 1

se os pontos são colineares ( mesma reta ) então vamos achar a reta que passa pelos pontos (2,1) e (4,-1) e por fim substituir o ponto que queremos descobrir .

Reta passando por (2,1) e (4,-1) :

$\displaystyle \sf y-y_o=m\cdot (x-x_o) \\\\ y - 1 = m\cdot (x-2) \\\\ \text{m = coeficiente angular }, \\\\ m = \frac{y_2-y_1}{x_2-x_1} \to m = \frac{-1-1}{4-2} \to m = \frac{-2}{2} \to m = -1 \\\\ Da{\'i}} : \\\\ y-1=-1\cdot(x-2) \\\\ y-1 = -x+2 \\\\ y = -x+2+1 \\\\ y = -x+3\\\\ \underline{\text{Substituindo o ponto (m,-2)}} : \\\\ -2 = - m+3 \\\\ m = 2+3 \\\\ \huge\boxed{\ \sf m = 5\ }\checkmark$