The following two right triangles are similar.If side PQ = 42, side LM = 28, and side QR = 24, what is the length of side MN?
1 answer:
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Given:
To find:
The value of x and measure of ∠A.
Solution:
Let C be angle the vertically opposite to ∠A.
The reference image for answer is attached below.
By vertical angle theorem:
m∠A = m∠C
m∠C = 10x + 24°
By the corresponding angle theorem:
m∠C = m∠B
Subtract 24° on both sides.
Subtract 6x from both sides.
Divide by 4 on both sides.
The value of x is 12°.
The measure of ∠A is 144°.
Consider two points in a two dimensional coordinate plane
As you know mid point of a line joining two points is the coordinate of the middle point of only that portion of line joining between two points.
[tex]\text { Mid point of } (x_{1},y_{1})\text { and } (x_{2},y_{2}) =(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]
As we know distance formula gives the Distance between line joining two points in two dimensional coordinate system.It is always positive.
[tex]\text { Distance formula between two points } (x_{1},y_{1})\text { and } (x_{2},y_{2}) =\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Distance formula gives the distance between two points, whereas Mid point formula gives coordinate of the middle point.
