HELP ME! WILL MARB BRAINLIEST FOR THE BEST ANSWER. PLEASE SHOW FULL SOLUTIONS. THANK YOU AND GOD BLESS.

2. Given triangle PQR where P(4,1),Q(a, 2a) and R(3,4). Solve for a if the equation of the altitude to side QR is y = −x + 6. You may want to draw a diagram.

The altitude is perpendicular to line QR, so point Q lies on a line through R that is perpendicular to the given altitude line. The given altitude line has a slope of -1. This means line QR will have a slope of 1, so the line QR in point-slope form is ...

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y -4 = 1(x -3)

Since point Q(a, 2a) is on this line, its coordinates will satisfy this equation.

2a -4 = a -3

a = 1 . . . . . . . . add 4-a to both sides

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The line with slope 2 on the attached diagram is the locus of all possible points Q. The one of interest is the one that is on the perpendicular through R.

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Additional comment

In order for a line to be an altitude to side QR, it must go through point P. The given line (y=-x+6) does not go through point P. We assume that the line y=-x+5 is the one that is intended.

HELP ME! WILL MARB BRAINLIEST FOR THE BEST ANSWER. PLEASE SHOW FULL SOLUTIONS. THANK YOU AND GOD BLESS. 2. Given triangle PQR where P(4,1),Q(a, 2a) and R(3,4). Solve for a if the equation of the altitude to side QR is y = −x + 6. You may want to draw a diagram.

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HELP ME! WILL MARB BRAINLIEST FOR THE BEST ANSWER. PLEASE SHOW FULL SOLUTIONS. THANK YOU AND GOD BLESS.

2. Given triangle PQR where P(4,1),Q(a, 2a) and R(3,4). Solve for a if the equation of the altitude to side QR is y = −x + 6. You may want to draw a diagram.