 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says find the point on x-axis which is equidistant from minus 2, 5 and 2 minus 3. So let us see the solution to this one. Since we have to find a point on x-axis so the coordinates of that point will be 0 where the abscissa is x and ordinate is 0 because the point lies on the x-axis so y will be 0. Now let the point minus 2, 5 with the point a and 2 minus 3 with the point b. Now we have to find this point which is equidistant from a and b that means we should have ac equal to bc. Now we find out ac then we find out bc and then we quit them. So using distance formula let us find ac first. Ac will be equal to under the root x minus minus 2 the whole square plus 0 minus 5 the whole square that is equal to under the root x plus 2 the whole square plus 25. Now we find out bc. bc will be equal to under the root x minus 2 the whole square plus 0 minus 3 the whole square that is equal to under the root x minus 2 the whole square plus 3 square is 9. Now we should have ac equal to bc so we equid these two now. So on equidding them we get under the root x plus 2 the whole square plus 25 is equal to x minus 2 the whole square plus 9 and this under the root. Now on squaring both sides we get under the root x plus 2 the whole square plus 25 becomes x plus 2 the whole square plus 25 and this becomes x minus 2 the whole square plus 9. So this implies x square plus 2x plus x square plus 4x plus 25 is equal to x square plus 4 minus 4x plus 9. Now we see that x square gets cancelled with x square 4 gets cancelled with 4 and we have 4x plus 4x equal to 9 minus 25 this further implies 8x is equal to minus 16. Now dividing both the sides by 8 we have x equals to minus 16 by 8. Now we divide the numerator and denominator by 8 and we get minus 2. So we have x equals to minus 2. So we simply put x equal to minus 2 in the point cx0. So vertices are minus 2 0 or we say that the point is minus 2 0 the point is 2 0 therefore the point c which has vertices minus 2 0 is equidistant from the point minus 2 5 and 2 minus 3. So our answer to this question is minus 2 0. I hope that you understood the question and enjoyed the session. Have a good day.