Equation of the line joining A(-1, 9) to B(6, 12)

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SUMMARY

The equation of the line joining points A(-1, 9) and B(6, 12) is determined using the slope formula, resulting in the equation y = (1/7)x + 64/7. A perpendicular line CD from point C(7, -5) intersects AB at point D, which can be calculated using the negative reciprocal of the slope of AB. The coordinates of point D are found to be (3, 10). Additionally, the distance from A to point M, defined as (K, -2K), is calculated using the distance formula, leading to the conclusion that K equals 2. The reflection of point (2, 9) across the line y = 2x is also computed, providing the coordinates of point Q.

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1.Find the equation of the line joining A(-1, 9) to B(6, 12).
Another line passes through C(7, -5) and meets AB at right angles at D.
Find the equation of CD and calculate the coordinates of D.

Given That the coordinates of M are (K, -2K) and that the distance of AM is [tex]\sqrt{178}units[/tex], calculate the value of K.

How do i calculate the value of K?

2. Q is the reflection of the point(2,9) in the straight line y = 2x. Calculate the coordinates of Q.
 
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omicron said:
1.Find the equation of the line joining A(-1, 9) to B(6, 12).
Another line passes through C(7, -5) and meets AB at right angles at D.
Find the equation of CD and calculate the coordinates of D.

Given That the coordinates of M are (K, -2K) and that the distance of AM is [tex]\sqrt{178}units[/tex], calculate the value of K.

How do i calculate the value of K?

|AM|^2=[(K+1)^2 + (-2K-9)^2] = 178 => K=2
2. Q is the reflection of the point(2,9) in the straight line y = 2x. Calculate the coordinates of Q.
If Q` is the reflection of Q about the line y=2x then the line y=2x is the perpendicular bisector of QQ`. QQ` has slope = -1/2 .Find the intersection pt.
which is the mid-pt of QQ`.

n:bugeye:b
 
Thanks...
 

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