Question

the vertices of △abc have the coordinates a(2, 4), b(1, 1), and c(4, -1). the vector <-6, -7> is used to translate △abc. which of the following are the coordinates of the image △abc? los vértices de △abc tienen las coordenadas a(2, 4), b(1, 1), y c(4, -1). el vector <-6, -7> se utiliza para traducir △abc. ¿cuáles de las siguientes son las coordenadas de la imagen △abc? a(-4, -3), b(-5, -6), c(-2, -8) a(8, 9), b(7, 8), c(10, 6) a(4, 3), b(5, 6), c(2, 8) a(-8, -9), b(-7, -8), c(2, 8) clear my selection

Explanation:

Step1: Translate point A

To translate point A(2, 4) using the vector <-6, -7>, we subtract 6 from the x - coordinate and 7 from the y - coordinate. So, \(x_{A'}=2+( - 6)=-4\) and \(y_{A'}=4+( - 7)=-3\), giving \(A'(-4,-3)\).

Step2: Translate point B

For point B(1, 1), \(x_{B'}=1+( - 6)=-5\) and \(y_{B'}=1+( - 7)=-6\), giving \(B'(-5,-6)\).

Step3: Translate point C

For point C(4, - 1), \(x_{C'}=4+( - 6)=-2\) and \(y_{C'}=-1+( - 7)=-8\), giving \(C'(-2,-8)\).

Answer:

A. \(A'(-4,-3),B'(-5,-6),C'(-2,-8)\)