Perhatikan gambar berikut: Tentukan persamaan garis yang: a. tegak lurus garis k, Dan melalui titik (-1,3) b. sejajar garis k, Dan melalui titik (0,5) TOLONG PA

Mencari gradien garis k

[tex]p(x1,y1) = p(3,0) \\ q(x2,y2) = q(0,2) \\ \\ m1 = \frac{y2 - y1}{x2 - x1} \\ m1 = \frac{2 - 0}{0 - 3} = - \frac{2}{3} [/tex]

Soal A; tegak lurus garis k melalui titik (–1, 3)

[tex]m1 \times m2 = - 1 \\ m2 = - \frac{1}{m1} \\ m2 = - \frac{1}{ - \frac{2}{3} } = - 1 \times ( - \frac{3}{2} ) = \frac{3}{2} \\ \\ y - y1 = m2(x - x1) \\ y - 3 = \frac{3}{2} (x - ( - 1)) \\ 2(y - 3) = 3(x + 1) \\ 2y - 6 = 3x + 3 \\ 2y = 3x + 9 \\ y = \frac{3x}{2} + \frac{9}{2} [/tex]

Soal B; sejajar garis k melalui titik (0, 5)

[tex]m1 = m2 \\ m2 = m1 = - \frac{2}{3} \\ \\ y - y1 = m(x - x1) \\ y - 5 = - \frac{2}{3} (x - 0) \\ 3(y - 5) = - 2(x) \\ 3y - 15 = - 2x \\ 3y = - 2x + 15 \\ y = - \frac{2x}{3} + 5[/tex]