Mixing
Finding Coordinates of a point on a line in Coordinate Grid.
Clash Royale CLAN TAG#URR8PPP
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To solve this question should I use Pythagoras rule like this?
Please, any other method to get the coordinates?
analytic-geometry
asked Jul 18 at 12:25
Dinesh Sunny
1688
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To solve this question should I use Pythagoras rule like this?
Please, any other method to get the coordinates?
analytic-geometry
asked Jul 18 at 12:25
Dinesh Sunny
1688
(1) Where did the $4$ and $2$ in your diagram come from? (2) Ignoring that whole approach, if the distance from $B$ to $C$ is $u$, what do you know about the distance from $B$ to $E$? You need to read the sentence about $E$ really carefully.
– John Hughes
Jul 18 at 12:28
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up vote
0
down vote
favorite
up vote
0
down vote
favorite
To solve this question should I use Pythagoras rule like this?
Please, any other method to get the coordinates?
analytic-geometry
asked Jul 18 at 12:25
Dinesh Sunny
1688
To solve this question should I use Pythagoras rule like this?
Please, any other method to get the coordinates?
analytic-geometry
asked Jul 18 at 12:25
Dinesh Sunny
1688
asked Jul 18 at 12:25
Dinesh Sunny
1688
asked Jul 18 at 12:25
Dinesh Sunny
1688
asked Jul 18 at 12:25
Dinesh Sunny
1688
1688
(1) Where did the $4$ and $2$ in your diagram come from? (2) Ignoring that whole approach, if the distance from $B$ to $C$ is $u$, what do you know about the distance from $B$ to $E$? You need to read the sentence about $E$ really carefully.
– John Hughes
Jul 18 at 12:28
add a comment |Â
(1) Where did the $4$ and $2$ in your diagram come from? (2) Ignoring that whole approach, if the distance from $B$ to $C$ is $u$, what do you know about the distance from $B$ to $E$? You need to read the sentence about $E$ really carefully.
– John Hughes
Jul 18 at 12:28
(1) Where did the $4$ and $2$ in your diagram come from? (2) Ignoring that whole approach, if the distance from $B$ to $C$ is $u$, what do you know about the distance from $B$ to $E$? You need to read the sentence about $E$ really carefully.
– John Hughes
Jul 18 at 12:28
(1) Where did the $4$ and $2$ in your diagram come from? (2) Ignoring that whole approach, if the distance from $B$ to $C$ is $u$, what do you know about the distance from $B$ to $E$? You need to read the sentence about $E$ really carefully.
– John Hughes
Jul 18 at 12:28
add a comment |Â
3 Answers
3
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Write the parametric equation of the line segment from $B$ to $C$:
$$(7(1-t)+9t,8(1-t)+4t)$$
The point corresponding to a fixed $t$ is $t$ of the way from $B$ to $C$. It follows that if $BC=frac23BE$ then $BE=frac32BC$, i.e. we substitute $t=1.5$ into the abobe equation and get $E=(10,2)$.
answered Jul 18 at 12:30
Parcly Taxel
33.6k136588
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Your picture is not correct. Point E should have been outside of BC
Otherwise you are on right track
answered Jul 18 at 12:33
Mohammad Riazi-Kermani
27.5k41852
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0
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First, you’ve gotten the order of the points incorrect. For $C$ to be $2/3$ of the way from $B$ to $E$ it must lie between those two points.
That aside, there’s no need to use the Pythagorean theorem for this. If the lengths of two segments of the same line are in a certain proportion, then the differences of their endpoint coordinates are in the same proportion. So, if $BC=frac23BE$, then $x_C-x_B=frac23(x_E-x_B)$ and $y_C-y_B=frac23(y_E-y_B)$. Plug in the known coordinate values and solve for the two unknown coordinates.
answered Jul 18 at 19:11
amd
25.9k2943
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Write the parametric equation of the line segment from $B$ to $C$:
$$(7(1-t)+9t,8(1-t)+4t)$$
The point corresponding to a fixed $t$ is $t$ of the way from $B$ to $C$. It follows that if $BC=frac23BE$ then $BE=frac32BC$, i.e. we substitute $t=1.5$ into the abobe equation and get $E=(10,2)$.
answered Jul 18 at 12:30
Parcly Taxel
33.6k136588
add a comment |Â
up vote
0
down vote
Write the parametric equation of the line segment from $B$ to $C$:
$$(7(1-t)+9t,8(1-t)+4t)$$
The point corresponding to a fixed $t$ is $t$ of the way from $B$ to $C$. It follows that if $BC=frac23BE$ then $BE=frac32BC$, i.e. we substitute $t=1.5$ into the abobe equation and get $E=(10,2)$.
answered Jul 18 at 12:30
Parcly Taxel
33.6k136588
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Write the parametric equation of the line segment from $B$ to $C$:
$$(7(1-t)+9t,8(1-t)+4t)$$
The point corresponding to a fixed $t$ is $t$ of the way from $B$ to $C$. It follows that if $BC=frac23BE$ then $BE=frac32BC$, i.e. we substitute $t=1.5$ into the abobe equation and get $E=(10,2)$.
answered Jul 18 at 12:30
Parcly Taxel
33.6k136588
Write the parametric equation of the line segment from $B$ to $C$:
$$(7(1-t)+9t,8(1-t)+4t)$$
The point corresponding to a fixed $t$ is $t$ of the way from $B$ to $C$. It follows that if $BC=frac23BE$ then $BE=frac32BC$, i.e. we substitute $t=1.5$ into the abobe equation and get $E=(10,2)$.
answered Jul 18 at 12:30
Parcly Taxel
33.6k136588
answered Jul 18 at 12:30
Parcly Taxel
33.6k136588
answered Jul 18 at 12:30
Parcly Taxel
33.6k136588
answered Jul 18 at 12:30
Parcly Taxel
33.6k136588
33.6k136588
add a comment |Â
add a comment |Â
up vote
0
down vote
Your picture is not correct. Point E should have been outside of BC
Otherwise you are on right track
answered Jul 18 at 12:33
Mohammad Riazi-Kermani
27.5k41852
add a comment |Â
up vote
0
down vote
Your picture is not correct. Point E should have been outside of BC
Otherwise you are on right track
answered Jul 18 at 12:33
Mohammad Riazi-Kermani
27.5k41852
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Your picture is not correct. Point E should have been outside of BC
Otherwise you are on right track
answered Jul 18 at 12:33
Mohammad Riazi-Kermani
27.5k41852
Your picture is not correct. Point E should have been outside of BC
Otherwise you are on right track
answered Jul 18 at 12:33
Mohammad Riazi-Kermani
27.5k41852
answered Jul 18 at 12:33
Mohammad Riazi-Kermani
27.5k41852
answered Jul 18 at 12:33
Mohammad Riazi-Kermani
27.5k41852
answered Jul 18 at 12:33
Mohammad Riazi-Kermani
27.5k41852
27.5k41852
add a comment |Â
add a comment |Â
up vote
0
down vote
First, you’ve gotten the order of the points incorrect. For $C$ to be $2/3$ of the way from $B$ to $E$ it must lie between those two points.
That aside, there’s no need to use the Pythagorean theorem for this. If the lengths of two segments of the same line are in a certain proportion, then the differences of their endpoint coordinates are in the same proportion. So, if $BC=frac23BE$, then $x_C-x_B=frac23(x_E-x_B)$ and $y_C-y_B=frac23(y_E-y_B)$. Plug in the known coordinate values and solve for the two unknown coordinates.
answered Jul 18 at 19:11
amd
25.9k2943
add a comment |Â
up vote
0
down vote
First, you’ve gotten the order of the points incorrect. For $C$ to be $2/3$ of the way from $B$ to $E$ it must lie between those two points.
That aside, there’s no need to use the Pythagorean theorem for this. If the lengths of two segments of the same line are in a certain proportion, then the differences of their endpoint coordinates are in the same proportion. So, if $BC=frac23BE$, then $x_C-x_B=frac23(x_E-x_B)$ and $y_C-y_B=frac23(y_E-y_B)$. Plug in the known coordinate values and solve for the two unknown coordinates.
answered Jul 18 at 19:11
amd
25.9k2943
add a comment |Â
up vote
0
down vote
up vote
0
down vote
First, you’ve gotten the order of the points incorrect. For $C$ to be $2/3$ of the way from $B$ to $E$ it must lie between those two points.
That aside, there’s no need to use the Pythagorean theorem for this. If the lengths of two segments of the same line are in a certain proportion, then the differences of their endpoint coordinates are in the same proportion. So, if $BC=frac23BE$, then $x_C-x_B=frac23(x_E-x_B)$ and $y_C-y_B=frac23(y_E-y_B)$. Plug in the known coordinate values and solve for the two unknown coordinates.
answered Jul 18 at 19:11
amd
25.9k2943
First, you’ve gotten the order of the points incorrect. For $C$ to be $2/3$ of the way from $B$ to $E$ it must lie between those two points.
That aside, there’s no need to use the Pythagorean theorem for this. If the lengths of two segments of the same line are in a certain proportion, then the differences of their endpoint coordinates are in the same proportion. So, if $BC=frac23BE$, then $x_C-x_B=frac23(x_E-x_B)$ and $y_C-y_B=frac23(y_E-y_B)$. Plug in the known coordinate values and solve for the two unknown coordinates.
answered Jul 18 at 19:11
amd
25.9k2943
answered Jul 18 at 19:11
amd
25.9k2943
answered Jul 18 at 19:11
amd
25.9k2943
answered Jul 18 at 19:11
amd
25.9k2943
25.9k2943
add a comment |Â
add a comment |Â
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(1) Where did the $4$ and $2$ in your diagram come from? (2) Ignoring that whole approach, if the distance from $B$ to $C$ is $u$, what do you know about the distance from $B$ to $E$? You need to read the sentence about $E$ really carefully.
– John Hughes
Jul 18 at 12:28