We could use the formula, derive the formula, or just work it out for this case. Let's do the latter.
The distance of a point to a line is the length of the perpendicular from the line to the point.
So we need the perpendicular to 5x-4y=10 through (-1,3). To get the perpendicular family we swap x and y coefficients, negating one. We get the constant straightforwardly from the point we're going through:
4x + 5y = 4(-1)+5(3) = 11
Those lines meet at the foot of the perpendicular, which is what we're after.
4x + 5y = 11
5 x - 4y = 10
We eliminate y by multiplying the first by four, the second by five and adding.
16x + 20y = 44
25x - 20y = 50
41x = 94
x = 94/41
y = (11 - 4x)/5 = 15/41
We want the distance from (-1,3) to (94/41,15/41)
Answer:
F=(-1, -2)
G=(-3, -5)
H=(-3, -2)
Step-by-step explanation:
Step-by-step explanation:
Since the two lines running left to right are parallel, and cut into the right side of the triangle, the angles and are equal.
With this information, we can solve for :
Now that we know , we can determine what the actual value of these angles are:
or
Now, we see that the top line of the two parallel lines cuts the right side of the triangle into two angles, and . Since it's cutting a straight line into two angles, we know that the same of these angles must be °. We already solved for the top angle and found that it is °, so that means the bottom angle is °. With this, we can solve for :
Therefore, the answer is
3×2+14=20
20×3+18=78
78×4+22=334
334×5+26=1696
1696×6+30=10206
Hence, the question mark should be replaced by 10206