A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]
B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)
<h3>A. How to determine the mid point</h3>
- Coordinate of C = (4, 5)
- Coordinate of D = (p, q)
- Mid point =?
Mid point = (X , Y)
X = (x₁ + x₂) / 2
X = (4 + p) / 2
Y = (y₁ + y₂) / 2
Y = (5 + q) / 2
Thus,
Mid point = (X , Y)
Mid point = [(4 + p) / 2 , (5 + q) / 2]
<h3>B. How to determine the coordinates of D</h3>
- Mid point = (7, 1)
- Coordinates of D =?
Mid point = (7, 1) = (X , Y)
X = (4 + p) / 2
7 = (4 + p) / 2
Cross multiply
7 × 2 = 4 + p
14 = 4 + p
Collect like terms
p = 14 - 4
p = 10
Y = (5 + q) / 2
1 = (5 + q) / 2
Cross multiply
1 × 2 = 5 + q
2 = 5 + q
Collect like terms
q = 2 - 5
q = -3
Coordinates of D = (p, q)
Coordinates of D = (10 , -3)
Learn more about coordinate geometry:
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There are 5 large dogs and 3 small dogs
<h3><u>Solution:</u></h3>
Let "S" be the number of small dogs
Let "L" be the number of large dogs
<em><u>Given that There are a total of 8 small and large dogs</u></em>
So we can frame a equation as:
number of small dogs + number of large dogs = 8
S + L = 8 ------- eqn 1
<em><u>You realize there are 2 more large dogs than small dogs</u></em>
Number of large dogs = 2 + number of small dogs
L = 2 + S -------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2 to find values of "L" and "S"</u></em>
Substitute eqn 2 in eqn 1
S + 2 + S = 8
2S + 2 = 8
2S = 6
<h3>S = 3</h3>
Substitute S = 3 in eqn 2
L = 2 + 3 = 5
<h3>L = 5</h3>
Thus there are 5 large dogs and 3 small dogs
Part a)
Time:distance
1:3
Part b)
6 hours
Part C)
81km
Answered by Gauthmath must click thanks and mark brainliest