Answer:
(c) 5y -17x +99 = 0
Step-by-step explanation:
The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.
<h3>Midpoint</h3>
The midpoint of XZ is the average of the coordinates of X and Z.
M = (X +Z)/2
M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)
<h3>Line through two points</h3>
The slope of the median can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
The slope of line YM is ...
m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
The line with slope 17/5 through point Y(7, 4) is ...
y -4 = 17/5(x -7)
Subtracting the right side, and multiplying by 5 gives ...
5(y -4) -17(x -7) = 0
5y -17x +99 = 0 . . . . equation of the median through Y
solution: option B and C both are correct i.e., option C is correct i.e., ∠E ≅∠H and ∠I ≅ ∠F .
option C is correct i.e., ∠E ≅∠H.
explanation:
it is given that ratio of corresponding sides of ΔFGE and ΔIJH are equal
i.e.,
and if ∠E ≅ ∠H
Then ΔFGE and ΔIJH are similar by SAS (side angle side) similarity theorem.
so option C is correct i.e., ∠E ≅ ∠H.
and option B is also correct
explanation:
since it is given that
And if ∠I ≅ ∠F
then ΔFGE and ΔIJH are similar by SAS (side angle side) similarity theorem.
9) inequality: 4+x>13 Solution: x>9
10) x+19 ≥ 8.2 ; x≥-10.8
11) (Sorry I don’t know what the question means by “interpret”) 17+x ≤ 26; Solution: x ≤9
12) 785+x≤1500; Solution: x≤715
