Question

Given A(4, 2) and B(-1, y) and the graph
of line t below, find the value of y so that
AB It.

Answer 1

Answer:

y = 9

Step-by-step explanation:

To solve this question we will use the property of perpendicular lines,

$m_1\times m_2=-1$

Where $m_1$ and $m_2$ are the slopes of two lines perpendicular to each other.

Slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of a line which passes through the points A(4, 2) and B(-1, y) will be

$m_1=\frac{y-2}{-1-4}$

     $=-\frac{y-2}{5}$

Slope of the line given in the graph [passing through (2, 4) and (-5, -1)]

$m_2=\frac{4+1}{2+5}$

$m_2=\frac{5}{7}$

From the property of perpendicular lines,

$\frac{-(y-2)}{5}\times \frac{5}{7}=-1$

$\frac{5(y-2)}{35}=1$

5y - 10 = 35

5y = 45

y = 9