5 2. Simplify . 5 O 57 O 5-1 o 5 O 57
1 answer:
You might be interested in
Question:
Consider ΔABC, whose vertices are A (2, 1), B (3, 3), and C (1, 6); let the line segment AC represent the base of the triangle.
(a) Find the equation of the line passing through B and perpendicular to the line AC
(b) Let the point of intersection of line AC with the line you found in part A be point D. Find the coordinates of point D.
Answer:
Step-by-step explanation:
Given
Solving (a): Line that passes through B, perpendicular to AC.
First, calculate the slope of AC
Where:
---
---
The slope is:
The slope of the line that passes through B is calculated as:
--- because it is perpendicular to AC.
So, we have:
The equation of the line is the calculated using:
Where:
---
So, we have:
Cross multiply
Make y the subject
Solving (b): Point of intersection between AC and
First, calculate the equation of AC using:
Where:
---
So:
So, we have:
and
Equate both to solve for x
i.e.
Collect like terms
Multiply through by 5
Collect like terms
Solve for x
Substitute in
Take LCM
Hence, the coordinates of D is:
