Find the value of x
2 answers:
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Answer:
1. √74; 2. (24.5, 21.5)
Step-by-step explanation:
1. Distance
You could use the distance formula to calculate the length of PQ, but I prefer a visual approach, because it requires less memorization.
Draw a horizontal line from P and a vertical line from Q until they intersect at R (28, 19).
Then you have a right triangle PQR, and you can use Pythagoras' theorem to calculate PQ.
2. Midpoint of line
The coordinates of the midpoint are half-way between the x- and y-coordinates of the end points.
For the x-coordinate, the half-way point is
(21 + 28)/2 = 49/2 = 24.5
For the y-coordinate, the half-way point is
(19 +24)/2 = 43/2 = 21.5
The coordinates of the midpoint M are (24.5, 21.5).
Since RS is a midsegment parallel to AC, that means R is the midpoint of AB and S is the midpoint of BC. The midpoint formula is:
. Using the coordinates of A and B, we have:
. Similarly, S is the midpoint of BC:
.
Since ST is a midsegment parallel to AB, then T must be a midpoint of AC:
.
Now that we have the coordinates of each point we can find the length of each segment using the distance formula:
For ST:
For RT:
For RS:
Since ST is a midsegment parallel to AB, then T must be a midpoint of AC:
Now that we have the coordinates of each point we can find the length of each segment using the distance formula:
For ST:
For RT:
For RS: