How to calculate coordinates of the intersection between the altitude and the base in a triangle.
$begingroup$
Given a triangle with vertices $A, B ;text{and}; C.$ The coordinates of these points are known upfront. Suppose we construct an altitude through $C$ and perpendicular to the line $AB.$ We will call the intersection point $D.$
Is there a formula with which I can calculate the coordinates of this point $D?$
EDIT: I need to program this somehow, so it would be handy if the formula only involved coordinates if possible.
Thanks in advance.
geometry triangle
edited Dec 31 '18 at 21:02
user376343
3,9584829
asked Dec 30 '18 at 1:37
Frederik VancloosterFrederik Vanclooster
83
$endgroup$
add a comment |
$begingroup$
Given a triangle with vertices $A, B ;text{and}; C.$ The coordinates of these points are known upfront. Suppose we construct an altitude through $C$ and perpendicular to the line $AB.$ We will call the intersection point $D.$
Is there a formula with which I can calculate the coordinates of this point $D?$
EDIT: I need to program this somehow, so it would be handy if the formula only involved coordinates if possible.
Thanks in advance.
geometry triangle
edited Dec 31 '18 at 21:02
user376343
3,9584829
asked Dec 30 '18 at 1:37
Frederik VancloosterFrederik Vanclooster
83
$endgroup$
add a comment |
$begingroup$
Given a triangle with vertices $A, B ;text{and}; C.$ The coordinates of these points are known upfront. Suppose we construct an altitude through $C$ and perpendicular to the line $AB.$ We will call the intersection point $D.$
Is there a formula with which I can calculate the coordinates of this point $D?$
EDIT: I need to program this somehow, so it would be handy if the formula only involved coordinates if possible.
Thanks in advance.
geometry triangle
edited Dec 31 '18 at 21:02
user376343
3,9584829
asked Dec 30 '18 at 1:37
Frederik VancloosterFrederik Vanclooster
83
$endgroup$
Given a triangle with vertices $A, B ;text{and}; C.$ The coordinates of these points are known upfront. Suppose we construct an altitude through $C$ and perpendicular to the line $AB.$ We will call the intersection point $D.$
Is there a formula with which I can calculate the coordinates of this point $D?$
EDIT: I need to program this somehow, so it would be handy if the formula only involved coordinates if possible.
Thanks in advance.
geometry triangle
geometry triangle
edited Dec 31 '18 at 21:02
user376343
3,9584829
asked Dec 30 '18 at 1:37
Frederik VancloosterFrederik Vanclooster
83
edited Dec 31 '18 at 21:02
user376343
3,9584829
asked Dec 30 '18 at 1:37
Frederik VancloosterFrederik Vanclooster
83
edited Dec 31 '18 at 21:02
user376343
3,9584829
edited Dec 31 '18 at 21:02
user376343
3,9584829
edited Dec 31 '18 at 21:02
user376343
3,9584829
3,9584829
asked Dec 30 '18 at 1:37
Frederik VancloosterFrederik Vanclooster
83
asked Dec 30 '18 at 1:37
Frederik VancloosterFrederik Vanclooster
83
asked Dec 30 '18 at 1:37
Frederik VancloosterFrederik Vanclooster
83
83
add a comment |
add a comment |
1 Answer
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$begingroup$
The slope of the altitude is opposite reciprocal of the slope of $AB$
You can find the equation of $CD$ using point slope formula and find the intersection of $AB$ and $CD$
answered Dec 30 '18 at 1:48
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
$endgroup$
add a comment |
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1 Answer
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$begingroup$
The slope of the altitude is opposite reciprocal of the slope of $AB$
You can find the equation of $CD$ using point slope formula and find the intersection of $AB$ and $CD$
answered Dec 30 '18 at 1:48
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
$endgroup$
add a comment |
$begingroup$
The slope of the altitude is opposite reciprocal of the slope of $AB$
You can find the equation of $CD$ using point slope formula and find the intersection of $AB$ and $CD$
answered Dec 30 '18 at 1:48
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
$endgroup$
add a comment |
$begingroup$
The slope of the altitude is opposite reciprocal of the slope of $AB$
You can find the equation of $CD$ using point slope formula and find the intersection of $AB$ and $CD$
answered Dec 30 '18 at 1:48
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
$endgroup$
The slope of the altitude is opposite reciprocal of the slope of $AB$
You can find the equation of $CD$ using point slope formula and find the intersection of $AB$ and $CD$
answered Dec 30 '18 at 1:48
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
answered Dec 30 '18 at 1:48
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
answered Dec 30 '18 at 1:48
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
answered Dec 30 '18 at 1:48
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
41.6k42061
add a comment |
add a comment |
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