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

y = 9

Explanation:

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

`m_1* 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=(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=(y-2)/(-1-4)`

`=-(y-2)/(5)`

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

`m_2=(4+1)/(2+5)`

`m_2=(5)/(7)`

From the property of perpendicular lines,

`(-(y-2))/(5)* (5)/(7)=-1`

`(5(y-2))/(35)=1`

5y - 10 = 35

5y = 45

y = 9