The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is
A.
√13
B.
3√2
C.
√26
D.
10√5
Correct Answer: 3√2
Explanation
P1 (4, 3), P2 (x, y)
y = 2x + 4 .....(1)
y = 7 - x .....(2)
Substitute (2) in (1)
7 - x = 2x + 4
7 - 4 = 2x + x
3 = 3x
x = 1
Substitute in eqn (2)
y = 7 - x
y = 7 - 1
y = 6
P2 (1, 6)
Distance between 2 points is given as
D =√ (x2−x1)2+(y2 − y1)
D = √(1−4)2+(6−3)2
D = √(−3)2+(3)2
D = √9+9
D = √18
D = √9×2
D = 3√2
P1 (4, 3), P2 (x, y)
y = 2x + 4 .....(1)
y = 7 - x .....(2)
Substitute (2) in (1)
7 - x = 2x + 4
7 - 4 = 2x + x
3 = 3x
x = 1
Substitute in eqn (2)
y = 7 - x
y = 7 - 1
y = 6
P2 (1, 6)
Distance between 2 points is given as
D =√ (x2−x1)2+(y2 − y1)
D = √(1−4)2+(6−3)2
D = √(−3)2+(3)2
D = √9+9
D = √18
D = √9×2
D = 3√2
