Topic 3&4 q. 8

Front

What is the formula to find the coordinates of a point that divides a line segment in a given ratio?

Back

If point P divides the line segment AB in the ratio m:n, then the coordinates of P are given by: P(x,y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where A(x1,y1) and B(x2,y2).

Front

Define the term 'ratio' in mathematics.

Back

A ratio is a relationship between two numbers indicating how many times the first number contains the second.

Front

What are the coordinates of Point A in the given problem?

Back

Point A is located at (-2, 6).

Front

What are the coordinates of Point B in the given problem?

Back

Point B is located at (1, 3).

Front

If Point P divides line segment AB such that AP/PB = 2/5, what is the total ratio of AP to PB?

Back

The total ratio is 2 + 5 = 7.

Front

How do you calculate the x-coordinate of point P when dividing a line segment in a ratio?

Back

Use the formula: Px = (m*x2 + n*x1) / (m+n), where m and n are the parts of the ratio.

Front

How do you calculate the y-coordinate of point P when dividing a line segment in a ratio?

Back

Use the formula: Py = (m*y2 + n*y1) / (m+n), where m and n are the parts of the ratio.

Front

What is the value of m in the ratio AP/PB = 2/5?

Back

m = 2.

Front

What is the value of n in the ratio AP/PB = 2/5?

Back

n = 5.

Front

Calculate the x-coordinate of point P using the coordinates of A and B and the ratio 2:5.

Back

Px = (2*1 + 5*(-2)) / (2+5) = (-8/7).