Question

I need help asap I took a picture of my question.

Answer 1

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m = slope

c = y intercept

The equation of the given line is

y = 2x + 4

By comparing both equations,

slope of the given line is 2

We would find a perpendicular line to this line passing through the given point. Recall, if two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line. This means that the slope of the perpendicular line passing through point K is - 1/2. We would find the y intercept by substituting x = 0, y = - 1 and m = - 1/2 into the slope intercept equation. We have

- 1 = - 1/2 * 0 + c

c = - 1

The equation of the perpendicular line is

y = - x/2 - 1

We would find the point of intersection by equating both lines. We have

2x + 4 = -x/2 - 1

Multiplying through by 2,

4x + 8 = - x - 2

4x + x = - 2 - 8

5x = - 10

x = - 10/5 = - 2

Substituting x = - 2 into the perpendicular line equation,

y = - - 2/2 - 1 = 1 - 1

y = 0

The point of intersection is (- 2, 0)

We would find the distance between K(0, - 1) and (- 2, 0) by applying the formula for finding the distance between two points which is expressed as

`\begin{gathered} \text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ x1\text{ = 0, y1 = -1} \\ x2\text{ = - 2, y2 = 0} \\ \text{Distance = }\sqrt[]{(-2-0)^2+(0-1)^2}\text{ = }\sqrt[]{4\text{ + 1}}\text{ = }\sqrt[]{5} \\ \text{Distance = 2.2}4 \end{gathered}`