Question

For the point P(21,19) and Q(28.24), find the distance d(P,Q) and the coordinates of the

Answer 1

d(P,Q) = 8.6023 units

Mid-point of PQ = (24.5, 21.5)

Further explanation:

Given

P(21,19) = (x1,y1)

Q(28,24) = (y1,y2)

We will use the distance formula to calculate d(P,Q)

The distance formula is:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\Putting\ values\ in\ the\ formula\\d = \sqrt{(28-21)^2+(24-19)^2}\\d=\sqrt{(7)^2+(5)^2}\\d(P, Q) = \sqrt{49+25}\\= \sqrt{74}\\= 8.6023$

The formula for midpoint is:

$M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\\= (\frac{21+28}{2}, \frac{19+24}{2})\\= (\frac{49}{2}, \frac{43}{2})\\= (24.5, 21.5)$

Keywords: Mid-point, distance between two points, coordinate geometry

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• brainly.com/question/10480770
• brainly.com/question/11015073

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Answer 2

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.

$\begin{array}{rcl}PQ^{2} & = & PR^{2} + QR^{2}\\& = & 7^{2} + 5^{2}\\ & = & 49 + 25\\& = & 74\\PQ& = & \mathbf{\sqrt{74}}\\\end{array}\\\text{d(P,Q) = \large \boxed{\mathbf{\sqrt{74}}} }$

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).