Question

On a radar screen, a plane located at A(-2,4) is flying toward B(4,3) Another plane, located at C(-3,1), is flying toward D(3,0). Are the planes' paths perpendicular? Explain.

Answer 1

Let's consider the screen of a radar as Descartes's coordinate plane (coordinates of points A, B, C, D are given). Further, points A(х_A , y_A), B(х_B , y_B),C(х_C , y_C), D(х_D , y_D) will look like

A(-2; 4);B(4; 3);C(-3;1);D(3;0);

(1 plane) y_A = k_AB*x_A + l_AB=> l_AB =- y_A + k_AB*x_A => y_A = k_AB*x_A + y_B - k_AB*x_Bk_AB = (y_A - y_B) / (x_A - x_B) => k_AB=(4-3)/(-2-4)=1/-6=-1/6
(2 plane) y_C = k_CD*x_C + l_CD => y_D = k_CD*x_D + l_CDl_CD = - y_D + k_CD*x_D =>y_C = k_CD*x_C + y_D - k_CD*x_Dk_CD = (y_C - y_D) / (x_C - x_D) => k_CD=(1-0)/(-3-3)=-1/6The slopes of plane's lines are equal

k_AB=k_CD => their paths are parallel