SOLUTION: The coordinates of the point P,Q,R are (-1,11),(2,5) and (t,3) respectively. Given that ∠PQR = 90 °, calculate the value of t. The line PQ is produced to S so that QS = PQ. Calc

Question 1178012: The coordinates of the point P,Q,R are (-1,11),(2,5) and (t,3) respectively. Given that ∠PQR = 90 °, calculate the value of t. The line PQ is produced to S so that QS = PQ. Calculate the coordinates of S.
Found 3 solutions by Solver92311, MathLover1, greenestamps:
Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!

If the measure of angle PQR is 90°, then the slope of segment PQ must be the negative reciprocal of segment QR.

Use the slope formula:

to calculate the slope of segment PQ. Calculate the negative reciprocal of the slope of segment PQ. Use the slope formula for segment QR with as a variable in the formula, set the formula equal to the negative reciprocal of the slope of segment PQ, and then solve for .

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

P,Q,R are ( , ),( , ) and ( , ) respectively

first find the slope of the line passes through
P( , ) and Q( , )

....use one point to calculate

.....eq.1

since given that ∠ °, find a line that is perpendicular to line with a slope and passes through Q and R

the slope of the perpendicular line will be negative reciprocal of the slope and it is

...use one point to calculate

.....eq.2
since given ( , ), we use line and the intersection point of the and will have
...substitute

=> and the point ( , )

given also: the line is produced to so that . Calculate the coordinates of .
will be on a line , from same distance as

distance is which is radius of the circle that passes through P, Q, and S
use the radius , draw a circle and read from the graph what are the coordinates of the point S

( , )

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Part 1: find t.

From P to Q is 3 units right and 6 units down; the slope of PQ is -2.

PQR is a right angle, so the slope of QR is +1/2. That means on QR the change in y is 1/2 the change in x -- i.e., the change in x is 2 times the change in y.

From Q to R the change in y is -2, so the change in x has to be -4. A change of -4 in x and a change of -2 in y from Q(2,5) puts us at R(-2,3).

ANSWER: t = -2.

Part 2: Find the coordinates of point S.

S is on PQ extended, and QS = PQ.

From P to Q was 3 units right and 6 units down; from Q to S will be the same.

3 right and 6 down from Q(2,5) puts us at S(5,-1).

ANSWER: S is (5,-1).

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