As shown in Figure 6, in the plane rectangular coordinate system, the three vertices of △ ABC are a (m, 4) B (6,0) C (- m, - 4), and AC passes through the origin o, BH is perpendicular to AC and H Find the value of AC * BH () to get the positive solution and offer a reward of 40

As shown in Figure 6, in the plane rectangular coordinate system, the three vertices of △ ABC are a (m, 4) B (6,0) C (- m, - 4), and AC passes through the origin o, BH is perpendicular to AC and H Find the value of AC * BH () to get the positive solution and offer a reward of 40

The slope of the straight line AC is k = 4 / m, it passes through the origin, then the linear equation of AC is: y = (4 / M) x, that is: 4x my = 0ac = √ [(2m) &# 178; + 8 & # 178;] = 2 √ (M & # 178; + 16) the distance from point B (6,0) to the straight line 4x my BH = | 4 * 6-0 | / √ (4 & # 178; + M & # 178;) = 24 / √ (M & # 178; + 16) so, ac * BH = 48