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Gre4nikov [31]
3 years ago
11

Please explain your answer. Thank you.

Mathematics
2 answers:
emmainna [20.7K]3 years ago
3 0

Answer:

See step-by-step

Step-by-step explanation:

PQ = PS .    Given

QR = SR .    Given

PR = PR .    Reflexive Property of Congruence

PQR = PSR   SSS Congruence Theorem

Vladimir [108]3 years ago
3 0

Answer:

(a) Used SSS congruence theorem.

(b) Orthocenter is (5,1)

Step-by-step explanation:

(a) We have given PQ = PS and QR = SR.

Also, due to commonly, the third side of each triangle is the same (PR)

We have the same side length for three sides of both triangles. Let's apply SSS congruence rule.

Thus, both triangles are congruent.

(b) Given data:

Y = (3,-2)

A = (3,5)

B = (9,1)

We need to construct at least two slopes of the line equations. Let's have m_{AB} and m_{YB}

m_{AB} = \frac{5-1}{3-9} = \frac{4}{-6} = -\frac{2}{3} \\m_{BY} = \frac{-2-1}{3-9} = \frac{-3}{-6} = \frac{1}{2}

Now, let's have the slopes for their respective orthogonal lines: m_{AN} and m_{YM}

Let's remember that the product of orthogonal slopes is -1. Thus, for examplem_{AN} m_{YB}=1 \\m_{YM} m_{AB}=1

We will use the coordinates of A and AN slope:

For AN m_{AN} = -\frac{1}{YB} = -2\\-2 = \frac{y-5}{x-3}\\ y = -2x + 11

This was the equation of AN.

Now, for YM, will use the coordinates of Y and YM slope:

m_{YM} = -\frac{1}{AB} = 3/2\\-3/2 = \frac{y+2}{x-3}\\ 2y-3x=13

This was for YM.

The orthocenter will be found by resolving the two-variable linear equation:y = -2x+11\\2y-3x=-13\\2(-2x+11) -3x=-13\\-4x+22-3x=-13\\-7x=-13-22=-35\\x=5\\y=-10+11=1\\

Thus, the orthocenter coordinates are (5,1)

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