A line intersects the y axis and x axis at the point P and Q respectively.If (2,-5) is the mid point of PQ,then the coordinates of P and Q are respecively
let P be (0,y) and Q be (x,0)
then (x+0)/2 = 2 ====> x = 4
and (y+0)/2 = -5 ====> y = -10
P is (0,-10)
Q is (4,0)
check by sketching
To find the coordinates of points P and Q, we need to use the information given:
1. The point (2, -5) is the midpoint of PQ.
2. Point P intersects the y-axis, which means the x-coordinate of P is 0.
3. Point Q intersects the x-axis, which means the y-coordinate of Q is 0.
Let's go through the process step-by-step:
Step 1: Determine the coordinates of the midpoint (2, -5).
The midpoint formula is given by:
(x1 + x2)/2 = x-coordinate of the midpoint,
(y1 + y2)/2 = y-coordinate of the midpoint.
In this case, the coordinates of the midpoint are (2, -5), so let's substitute the values into the formula:
(x1 + 0)/2 = 2, and (y1 + 0)/2 = -5.
Simplifying these equations:
x1/2 = 2,
y1/2 = -5.
Multiplying both sides of each equation by 2, we get:
x1 = 4,
y1 = -10.
So, P has coordinates (4, -10).
Step 2: Determine the coordinates of point Q.
From the given information, we know that Q has an x-coordinate of 0 and a y-coordinate of 0.
Therefore, Q has coordinates (0, 0).
In conclusion, the coordinates of points P and Q are respectively (4, -10) and (0, 0).